MATHEMAGICS FOR STAR-KIDZ WORKBOOK
Jain 108
SACRED GEOMETRY AFTER SCHOOL CLASSES MULLUMBIMBY OCTOBER 2014
LEARN SACRED GEOMETRY WITH JAIN 108. + MATHEMAGICS CLASSES For CHILDREN & ADULTS Of ALL AGES
JAIN 108's 21st CENTURY CURRICULUM 2014 Classes after school include: invites You and Your Child to: Mathemagics For StarKids (5 to 8 years old) • Learn how to multiply numbers at the Starts Tuesday 7th October, 2014 Time 3.20pm to Speed of Thought. 4.30pm. • Become a Mathematical Genius. 4 Tuesdays in October. One Parent to be present. • Improve your Mathematical Confidence. • Improve your Memory Power. Mathemagics For Juniors (9 to 12 years old) • Build the Mental Muscle! Starts Wednesday 8th October, 2014. Time 3.20pm to • Learn about Magic Squares, the Fibonacci 4.30pm. Sequence, Fractal Geometry and the 5 4 Wednesdays in October. One Parent to be present. Platonic Solids. • Translate Numbers Into Art. Mathemagics For Teens (13 to 19 years old) • This New Maths is the emerging curriculum Starts Thursday 9th October, 2014. Time 3.20pm to for the Earthheart School or Sacred 4.30pm. Geometry University. 4 Thursdays in October. Adults are welcome as paid • Certificate Accredited Courses issued per students in this class. School Term. Bookings are essential. $20 per class. Link: http://www.jainmathemagics.com/page/11/ default.asp A commitment to these 4 classes involves a payment of $80 before the 1st October.
All enquiries for Term 4, 2014, call Jain 108 on 02 6684 4409 or 0423 583 886
VENUE: AT THE LIVING YOGA SANGA (first floor, 63 Stuart Street. above Mullum Mac in Mullumbimby 2482, Far North N.S.W, inland of Byron Bay)
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 1
CONTENTS
LESSON TITLE PAGE
1 Drawing Circles. 4 + Weaving Semi-Circles Free-Hand
2 Triangle Numbers. 22 + Tetrahedron Numbers
3 Square Numbers. 29 + Cube Numbers (Cubic Number Patterns)
4 The Magic Square of 3x3 Lo-Shu Pattern 37 + Rotating it upon itself at a 90 Degree Rotation
5 Pentagrams. 48 Drawing Freehand the Uni-Cursal Pentagram + Embedding the Pentacle Within Itself.
6 Hexagrams. 55 + The Star of David + Drawing Free-hand the Uni-Cursal Hexagram (Without Taking Your Pen Off The Paper) + Mystic Rose
7 Cube Combinations. 66 + Exploring Wooden Cubelets or Square Tiles: Number Patterns or Permutations.
8 String Art 77
9 Creation of the 7-Circuit Labyrinth 79
10 Promotional Posters 85
nb: There is a blank page at the end of each chapter, to be used for notes or for any free use of creative outbursts or realizations or memos.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 2 Front Cover: Picture of Starzi Porter, at 8 years of age, holding a circular piece of String Art that she spontaneously weaved upon a breadboard with 12 nails, in October 2014 in Mullumbimby when we covered 9 weeks of After-School classes. This content is repeated during Term 2 of 2015, but also new content for Term 2 will be offered, an exciting 9 week / 9 Lesson course on the 5 Platonic Solids.
Mathemagics 4 Star Kidz Code Name = M4SK
INTRODUCTION:
These following Lesson Plans are the script to make a video to fulfill a need for a new curriculum for Star Kids, aged 5 to 8 years old, for the International Home Schooling Movement. It essentially is a guide for Parents to introduce their child to the basic geometric concepts that is suitable for this age group. This booklet will be followed by another book and video called Mathemagics 4 Juniors (ages 9 to 12 year olds), Code Name = M4J. This in turn will be followed by another book and video called Mathemagics 4 Teens (ages 13 to 19 year olds), Code Name = M4T.
The symbolism of this booklet’s content is based on the fact that the first and last chapters are based on the Circle, which is the beginning or source of Form. Chapter 1 is Drawing The Circle, and Chapter 8 is Circular String Art + Chapter 9 on the circular 7-circuit Labyrinth. This means that the actual subjects or contents are based on Form: that is, on the line, triangle, square, pentagon, hexagon, constitute a genuine journey beginning from The Source or The Zero or The Circle, progressing from the 3 to the 4 to the 5 to the 6 of Form, of the worldly aspect, and returns back to the infinity of the Circle represented by String Art.
Any contributions to the improvement of this material is welcomed.
The putting together of this rare and original syllabus has been a fantastic challenge for me, being forced to write content for the youngest level of the enquiring mind, asking myself, how is it that an innocent Child truly learns. Usually I am cracking cryptic codes and working on high level algebraic equations, so this simple and evolving Miniversity has kept the target real and focussed . I remember as a child myself, running up and down large flight of steps, at the age of 3 or 4, was a fun exercise in counting. I realized over the years that this is a natural aspect of learning, not just an intellectual endeavour. Even in the womb a child is engrossed in staring at its own webbed fingers, in total fascination, observing 5 distinct emanations coming from itself. I know that some spiritually-based schools of thought like the Anthroposophical Waldorf or Steiner schools may disagree with the concept of teaching a Child maths before the age of 7, but from my direct observations, Children love numbers and geometry, no matter what age they be. Put your Child through this course and see for yourself how much they love it.
Produced and Printed in Mullumbimby Creek, Far North NSW, 2482, Australia.
♥ Jain 108 Mathemagics ♡ © Copyright, 2015
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 3
LESSON 1 DRAWING CIRCLES AND WEAVING SEMI-CIRCLES FREE-HAND
Lesson 1 Synopsis or Summary of the Lesson
1 – Drawing Circles Free-Hand. As a guide, Circles of 24 Dots (IcosaTetraGon), then 12 Dots (Dodecagon) then 6 Dots (Hexagon) then 5 Dots (Pentagon) are supplied.
2 – Drawing Semi-Circles, alternating above and below the Line. Using both Right and Left Hand.
3 – Drawing Alternating Semi-Circles in circles of 4 Dots, 6 Dots, 12 Dots, 24 Dots
4 – Drawing Alternating Semi-Circles in circles of 3 Dots, 5 Dots, 17 Dots, 9 Dots, starting both Inwardly and Outwardly to produce differing patterns.
5 – The Cross of Alternating Semi-Circles: Rhythm Drawing
Preparations Before Lesson 1 Starts
Ø Name Introductions by throwing ball around, if time permits: stating :
My name is ………………..………… and my favourite fruit is ………….………….
This also teaches Memory Power by using an association with an Image. eg, the 4th Person in the circle of say 10 students, would say, reciting from memory the favourite fruit of the 4th, then the 3rd, then the 2nd, would say: Lou loves mangoes, Amala loves strawberries, Marcus loves passionfruit, my name is Germaine and I love pawpaw.
Also have NAME CARDS, made of cardboard, placed on the tables, each student’s name is written in calligraphy in front of each student, for the benefit of both Teacher and Students.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 4
PART 1: DRAWING CIRCLES Free-hand
Start the lesson by drawing a circle, to acquaint the Child with a Compass, lots of practice drawing circles free hand. Rulers are not necessary.
Here is a Circle with 24 Dots. Trace the dots in a smooth fashion to create your circle. Best to start from the very top dot (north of the compass, or the zenith point).
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 5
Join The Dots to make smooth circles.
Here is a Circle with 12 Dots, join the dots, to trace a smooth circle.
Here is a Circle with 6 Dots, join the dots, to trace a smooth circle.
Here is a Circle with 5 Dots, join the dots, to trace a smooth circle.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 6
In the blank spaces above, practice 12 circles, free-hand. Notice the first 6 Circles are visible but very faint, to get you started. Practise using your Left Hand or Other Hand not normally used, on some of the circles.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 7 PART 2: DRAWING AND WEAVING SEMI-CIRCLES
Can you the see the semi-circles or half-circles in the pictures below.
Practice your semi-circles, drawing one above the line, and the next one below the line, alternating the semi-circles: upright, then upsidedown, upright then upsidedown, etc.
Solution
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 8
Starting from the Right and proceeding to the Left, use your other hand to draw the same fluid sequence of semi-circles.
Here are 4 Dots that form the Square or Diamond. Can you start from the topmost zenith point or dot, and draw your alternating semi-circles in a fluid line. Start with the first Semi- Circle going in an outward direction. Keep drawing till you reach the point from where you started. Place a Dot in the Centre of the Circle, called the CentrePoint, as 2 inward semi-Circles must touch this CentrePoint.
Diamond of 4 Dots Diamond of 4 Dots. Use Your Other Hand!
It doesn’t matter which way you start weaving your semi-circles, whether you start from the outside, or from the inside, both pathways give the same result. nb: the two semi-circles that go inwards must touch the centre of the circle or Centrepoint! Solution to Diamond of 4 Dots
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 9
Pentagram of 6 Dots There are 2 ways to start your first semi-circle. Try your first semi-circle going outside the circle of dots, and on your next dots, try your first semi-circle going inside the circle of dots.
6 Dots: Solution
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 10
Solutions to Weaving Alternating Semi-Circles Upon circles with 3, 4, 5, 6, 7, 8, 9, 10 and 16 equally spaced Dots
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 11 Circle of 12 Dots Now that you are practiced, use your Right Hand, to weave Semi-Circles, in and out, in a fluid motion. Let your smooth line dance and flow.
Circle of 12 Dots Now that you are practiced, use your Left Hand, to weave Semi-Circles, in and out, in a fluid motion. Let your smooth line dance and flow.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 12
Circle of 24 Dots Now that you are practiced, use your Best Hand, to weave Semi-Circles, in and out, in a fluid motion. Let your smooth line dance and flow.
Here is a . Can you copy the curves of these curving scrolls / embellishments / flourishes, or create something new and similar?
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 13 OPTIONAL: WEAVING SEMI-CIRCLES FROM ODD-NUMBERED POLYGONS: 3, 5, 7 & 9 These next exercises are a little bit more challenging that what has already been given, it is only presented for a deeper understanding of Creative Design. The students are also being challenged to follow specific instructions and asked to recall this set of information, how to draw a certain diagram, to develop their memory skills and memory power.
DRAW SEMI-CIRCLES IN TRIANGLE: START OUTWARDLY
Here are 3 Dots that form the Triangle. Can you start from the topmost zenith point or dot, and draw your alternating semi-circles in a fluid line. Start with the first Semi-Circle going in an outward direction. Keep drawing till you reach the point from where you started. In the second space, draw it again with your left hand if you like.
Triangle of 3 Dots Start Semi-Circle outwardly. On the right, the Solution neatly drawn with a set of compasses, and marking midpoints of the triangles.
With your 3 Dots, can you practice some artistic pictures. Here are 2 examples:
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 14 DRAW SEMI-CIRCLES IN TRIANGLE: START INWARDLY
Here are 3 Dots that form the Triangle. Can you start from the topmost zenith point or dot, and draw your alternating semi-circles in a fluid line. Start with the first Semi-Circle going in an Inward direction. Keep drawing till you reach the point from where you started. In the second and third space, draw it again with your left hand if you like. Is it a different pattern than the one that started with outward semi-circles?
solution
Triangle of 3 Dots. Midpoints of the 3 edges of the Triangle are marked. The 3 Semi-Circles, starting Inwardly. They have been drawn precisely with a compass to show the true form of the elegant solution.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 15
DRAW SEMI-CIRCLES IN PENTAGON: BOTH INWARDLY AND OUTWARDLY
There are 2 ways to start your first semi-circle. Try your first semi-circle going outside the circle of dots, and on your next dots, try your first semi-circle going inside the circle of dots.
Semi-Circles, starting from zenith, Semi-Circles, starting from zenith, starting outwardly. Drawn precisely with a starting inwardly. Drawn precisely with a set of compasses. set of compasses.
5 Dots drawn freehand, starting outwardly : Solution sketched.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 16
SEMI-CIRCLES In SEPTAGON (7-sides) drawn both INWARDLY and OUTWARDLY
Septagon of 7 Dots, Septagon of 7 Dots, Semi-Circle has started Outwardly. Semi-Circle has started Inwardly. Solution drawn neatly, with a set of Solution drawn neatly, with a set of compasses, and marking the midpoints of compasses, and marking the midpoints of the 7 sides. the 7 sides.
SEMI-CIRCLES In NONAGON (9-sides) drawn both INWARDLY & OUTWARDLY
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 17 THE CROSS OF ALTERNATING SEMI-CIRCLES
(Rhythm Drawing)
Here is a final task, that involves the use of all that you have learnt, essentially to keep drawing with a flow, not taking your pencil off the paper, to produce this freeform cross with ever-expanding end-sections. This is a good test for remembering a set of instructions and improving confidence with Rhythm Drawing. A set of instructions is called an Algorithm, no different than a cake recipe.
Shown in the table below are 7 steps or rules that must be followed. Use only a lead pencil first, but when it is complete, you can retrace the two parts with 2 colours.
THE 7 STEPS TO CREATE YOUR CROSS
Step 1)- The basic skeleton form of the cross are the 4 basic Compass Points (North, South, East and West) surrounding a Central 5th Point around which everything will flow. These 5 Points can not be touched by pencil at any time. Only draw curves or semi-circles around them.
Step 2)- One Pathway will be Vertical, the other Horizontal. Each Pathway looks like 3 touching circles or a like a figure 8 but with 3 sections. Begin with the Vertical Pathway. Start at the zenith and begin to draw alternating semi-circles around the 3 Points.
Step 3)- The first Pathway is complete. Go over this 3x to get a rhythm of flow happening, making sure that your pen or pencil does not go off the paper, ie: you are tracing this shape 3 times, as if to make it bolder.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 18
Step 4)- When ready, extend growing curves above the North Point and below the South Point, again do not take your pencil off the paper, each curve is about a millimeter apart. The curve goes south then north then south then north until it is complete. Your drawing is a fluid, non-stopping action. The 2 rules here a)- you must trace exactly over the semi-circles around the Centre Point, and b)- you must draw only 5 extra arcs or extended curves at both the North and South Points. Now that you have done this in pencil, you can
choose one colour to retrace this Vertical Pathway. You are now halfway to completing this fancy Cross.
Step 5)- Pick up your lead pencil and get ready to complement what you have just drawn. You will draw the same pattern again but horizontally. Start from the left of West Point and begin to alternate your semi-circles.
Step 6)- The first Horizontal Pathway is complete. Go over this 3x to get a rhythm of flow happening.
Step 7)- Same as Step 5)- and not including the first curve just drawn, draw another 5 extended arcs at both West and East Points without taking your pencil off paper, without stopping until all arcs are drawn. Now that you have done this in pencil, you can choose another colour to retrace this Horizontal Pathway.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 19
In the 4 spaces below, you have 4 attempts to practice this Cross. In the last space, you may want to come up with your own Pathway or Design.
(Torus, fractally embedded within itself)
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 20 Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 21
LESSON 2 TRIANGLE NUMBERS + TETRAHEDRON NUMBERS
Lesson 2 Synopsis or Summary of the Lesson
1 – Start with a bag of 27 wooden blocks.
2 – Triangle Numbers from 1 to 5
3 – Drawing around faint circles to form the first 4 Triangle Numbers
4 – Charting Triangle Frequency that generate the Square Number Sequence
5 – Draw the Tetrahedron freehand over the faint lines given
6 – Counting how many spheres in multi-layered Tetrahedra
7 – Charting the Tetrahedron Numbers from 1 to 5
8 – Puzzle: Using a string, locate a square plane inside a 3-dimensional tetrahedron made out of wooden doweling and soft-plastic-tubular joins.
9 – If time permits, using this string to join the 6 midpoints of the 6 edges of Tetrahedron to create the Octahedron (8 triangles) that exists inside.
10 – If time permits, using this string to join the 4 face-centres of the 4 Triangular Faces of the Tetrahedron to show that a smaller and inverted Tetrahedron exists inside, (called the Dual, and in this case, the Self-Dual) generating the definitions of Self-Similarity and Fractal (when the inside is the same as the outside).
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 22
Basic Principles:
✪ Start with a Bag of 27 wooden cubic blocks (The parent can create a lesson with the child how to make their Magic Bag, to place importance on the fact that it will carry their first 27 marbles or cubic blocks..)
PUZZLE: With 27 blocks or cubelets, what is the most compact or smallest shape possible when we squash or compress all 27 cubes? What do we call this shape?
✪ Teach the first Triangular Numbers
* * * * * * * * * * Tetraktys. These 10 Dots were the symbol of The 10 dots of Tetraktys create the 5 Pythagoras, creating the Universe Platonic Solids.
This is the idea of 1 + 2 = 3 and 1+ 2 + 3 = 6 and 1+ 2 + 3 + 4 = 10
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 23 The revelation of the Triangle Numbers is perhaps the simplest form of Number Progression. It is asking the child in a coherent manner: “What is 1? What is 1+2? What is 1+2+3? What is 1+2+3+4? etc…
Next, you may want to record this information as a Sequence: 1 – 3 – 6 – 10 – ? and them ask them what is the next Triangle Number? (15)
You may want to chart or table this info for the 7 or 8 year old:
Triangle Number Sum of Numbers Final Sum
1 1 1
2 1 + 2 =
3 1 + 2 + 3 =
4 1 + 2 + 3 + 4 =
5 1 + 2 + 3 + 4 + 5 =
Draw around these Circles to form the first 4 Triangle Numbers.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 24
TRIANGLE FREQUENCY
1 Frequency 2 Frequency 3 Frequency 4 Frequency Triangle Triangle Triangle Triangle
Can you draw these 4 Triangles by tracing over the faint lines below?
Frequency How Many Little Square Number Triangles?
1 = 1 = 1 x 1
2 = 4 = 2 x 2
3 = =
4 = =
Did you know, that the sum of these Little Triangle Numbers form Square Numbers!
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 25
Tetrahedron = 3-dimensional Triangle Draw this freehand
✪ Get the student to draw the Tetrahedron freehand, starting from the largest outer Triangular, place the central bindu dot, then join 3 shorter lines from the centre towards the 3 corners of the large outer triangle. Observe the 6 lines or edges.
✪ Teach how the Triangle and therefore the Tetrahedron is the most stable shape, compared to the Cube or Box or Square. Let the Children know that
Draw the 4 circles or sphere Once You were a Shape, known The centre of 4 Spheres, when outlines that define the as the Tetrahedron, at 4-cell joined, generates the Tetrahedron (1 sphere sitting division of the zygote! Tetrahedron. upon the valley of 3 spheres).
How many Spheres are there in this 3 How many Spheres are there in this 5 layered Tetrahedron? …………… layered Tetrahedron? …………….
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 26 You may want to chart or table this info for the 7 or 8 year old:
Tetrahedron Sum of Triangle Numbers Sum of Balls in the Tetrahedron Number
1 1 = 1
2 1 + 3 =
3 1 + 3 + 6 =
4 1 + 3 + 6 + 10 =
5 1 + 3 + 6 + 10 + 15 =
PUZZLE: Inside a Tetrahedron, there is a secret Square shape. With this yellow flouro string, can you find this square? Clue. Wrap the string around 4 of the 6 possible midpoints. A midpoint of an edge is the middle point or half way mark. This Square is actually part of another 3- dimensional shape (the Octahedron or 3-dimensional Diamond).
Symbolically, this represents the progression from 3-ness to 4-ness. (Later, when the cube of 4-ness is tilted in a certain way, what appears is 5-ness of the Dodecahedron having 12 pentagonal faces).
The “Impossible Triangle” and the Dual of the Tetrahedron (Joining the 4 Face Centres) is itself. Notice how the continuation of this Dualing, creates an alternation of Up and Down or Oscillation. For this reason, it is called Self-Similar or Fractal.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 27
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 28
LESSON 3 SQUARE NUMBERS + CUBE NMBERS (CUBIC NUMBER PATTERNS)
Lesson 3 Synopsis or Summary of the Lesson
1 – Drawing over faint circles to make the Square Numbers
2 – Chart of Square Numbers from 1 to 5
3 – Demonstrate how the Tetrahedron is more stable than the Cube
4 – Identifying the names of the Cubes from 2x2x2 to 6x6x6
5 – Drawing the Cubes up 3x3x3 over faint lines
6 – Dual of the Cube is the Octahedron (joining the 6 face-centres)
7 – The 8 Original Cells
8 – The Star Tetrahedron
9 – Identifying the Tetrahedron that exists inside the Cube
th 10 – Activity using Zometool parts. Glue the 6 Cubes glued around a central 7 cube to create the 12-Diamond shape (Rhombic Dodecahedron) by joining the 6 centres of the 6 cubes
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 29
✪ Teach the first Square Numbers, using the wooden blocks ie: 2x2 = 4 3x3 = 9 4x4 = 16 5x5 = 25
This is called a 3x3 Square = 3 + 3 + 3 = 9
Can you draw over the faint Circles above to make the square numbers
What do we call this pattern? ……………………......
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 30 Next, you may want to record this information as a Sequence: 1 – 4 – 9 – 16 – 25 ? and them ask them what is the next Square Number? (36)
You may want to chart or table this info for the 7 or 8 year old:
Square Number Sum of Numbers Final Sum
1 1 x 1 = 1
2 2 x 2 =
3 3 x 3 =
4 4 x 4 =
5 5 x 5 =
✪ Teach the Family of Odds and Evens (Optional).
What do you call a Square that is tilted to one side? ………………………………
✪ Teach the Sequence of 3-Dimensional Numbers or Cubic Numbers: 1, 8, 27, 64, …
1x1x1
Complete the names of the above cubes.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 31
Can you give names
for all the cubes eg: 4x4x4 or 5x5x5x or 6x6x6 ?
✪ (nb: This is why we begin with 27 cubelets of wooden blocks, to realize that 3 cubed = 27 =3x3x3 = 3^3 = 33).
(Also, on a cosmic level, the number 27 is critically important in understanding the Mathematics of Harmonics, the most important one is the Binary of 27: which is the doubling of 27 continuously: 27 - 54 - 108 - 216 - 432 - 864 etc cosmological numbers that appear as the radii of the earth, sun and moon etc… Numbers of time also appear. eg: there are 86,400 seconds in a day )
✪ Teach how the Triangle and therefore the Tetrahedron is the most stable shape, compared to the Cube or Box or Square. When you sit on a cubic box, it tends to slant, and is therefore unstable, as explained by Buckminster Fuller, father of domes. That is why the Tetrahedron is the basic building block of atomic structure.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 32 DRAWING THE
✪ Teach the children how to draw a single cube, then a 2x2x2 cube, then a 3x3x3 cube.
Draw this 1x1x1 solid- looking cube.
Draw this 1x1x1 Cube that is transparent, ie: we can see through it.
Draw this 2x2x2 solid-looking cube.
Draw this 3x3x3 solid-looking cube.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 33
What would we call this These other diagrams are all related to this original 2x2x2 shape? Cube or Vessel of Creation.
Question: or Puzzle:
Is it a Cube missing one Corner or a Corner with
a Cube in it? The Dual of the Cube is the Star at this for a little Octahedron (8 Triangles) formed by joining the 6 Face Centres. while.
Did You Know, that this is what you looked like in the first hour of your life, before you were even born, from the moment of your Conception, when Father- Mother made Love and
Created You. It is called “The 8 Original cells” or 2 Cubed: 2x2x2.
The 8 tips or vertices of the Star tetrahedron or Stella Octangula (as Leornardo da Vinci called it) join to form the humble Cube Tetradedron inside of the cube
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 34 ACTIVITY USING ZOMETOOL PARTS
This final activity, to understand the deeper nature of the cube and how it maps space, is to have 7 cubes, all the same size and somehow join or glue 6 cubes around the central 7th. The diagrams show how this will look. I suggest ordering the large blue sticks from Zometool in Colorado, USA, a large and growing supplier of educational toys. (Their website is: www.zometool.com). To give you an understanding of what zometool structures look like, have a look at the other graphic called the Rhombic Dodecahedron, which is what these 7 cubes make, when magic spider weaves its thread from the 6 centres of the 6 outer cubes, connecting 6 pyramid-like shapes to the central 7th cube. This shape formed is RHOMBIC DODECAHEDRON (Rhombic means “diamond” and Dodeca means “2+10=12) ie: a 12 diamond shape.
7 CUBES MAKE A 12 DIAMOND SHAPE
Zometool rods and 6 Cubes around connectors make many a central 7th. educational shapes
Fusing a Cube with the Octahedron also makes the Rhombic Dodecahedron “Snowman” made from Zometool.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 35 Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 36
LESSON 4 MAGIC SQUARE OF 3X3 LO-SHU PATTERN
Lesson 4 Synopsis or Summary of the Lesson
1 – Definition of the Magic Square of 3x3. Sums of 3 columns and 3 rows and 2 diagonal sum to 15. Use 9 playing cards to demonstrate the beauty of this ancient puzzle
2 – Show how the opposing pairs sum to 10
3 – Drawing the Magic Square once, @ 0°
4 – Super-imposing the same Magic Square upon itself at right angles: 0° + 90° using two different colours
5 – Show the Magic Square rotated upon itself 4 times (4x45°) to create my logo and 8 times ((8x22.5°)
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 37 Now that the child has learnt that Numbers are Shapes, and they know their first 9 numbers, they are ready to construct their first Magic Square of 3x3. You will need a large board about 500mm x 500mm, 9 nails, two colours of string, ruler 300mm length, lead pencil, colour pencils.
6 1 8 7 5 3 2 9 4
PART ONE THEORY
In this lesson, they have to look at 1 - All the Pairs of 10 opposing the central cell 5 2 - All the Sums of the 3 Columns, 3 Rows and 2 Diagonals, what do they add up to?
To assist in their counting, best to use large balls, say billiard balls. Remind them when patterns appears eg: the number 10 is a Triangular Number (being the sum of 1+2+3+4) and let them form it again. 3 - The child constructs on their own chart paper, with the help of their parent, the empty 3x3 frame of 9 cells:
Show them the 9 Dots in a Square come from the 9 Centres of the 9 Squares.
The numbers of the Magic Square from 1 to 9 are written into their correct places.
The child is encouraged to draw their first pattern in lead pencil first, then when it is finished, they can use their favourite colour to go over the lines again.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 38
Here is an example of a finished Magic Square of 3x3 Pattern, done with string on board, originally starting with 9 nails. String Art is a very popular medium for StarKidz. Ideally, your child can draw the patterns on the board with string, then draw it in their book.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 39
MAGIC SQUARE OF 3 DRAWN ONCE
DRAWING THE MAGIC SQUARE ONCE (AT ZERO DEGREES): On the next page, the child will draw the pattern once, as shown above, ensuring to connect the last number “the number 9” to “the first number 1”. Explain to the child that these lines are like lines of electricity, and by connecting the Alpha to the Omega, they are creating a circuit board, of energy or electricity that can now flow forever.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 40
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 41
SUPER-IMPOSING THE SAME MAGIC SQUARE UPON ITSELF: On the next page, the child will draw the pattern once, as shown above. Use pencil first, to draw the first pattern, then colour it in. Then turn this page aground at a 90 degree angle so that the tilted numbers of the magic square on the bottom of this page are standing vertical. Again, in pencil, draw the same pattern again. You are super-imposing the same magic square yantra (pattern) upon itself at a 90 degree angle. (Explain the 90 degree angle as quarter turn of the circle or the shift from Vertical to Horizontal). When this is drawn correctly, choose a second favourite colour and go over these pencil lines.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 42
MAGIC SQUARE OF 3 (LO-SHU) DRAWN TWICE (O° + 9O°) SUPER-IMPOSED UPON ITSELF AT A 90 DEGREE ROTATION
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 43
MAGIC SQUARE OF 3 (LO-SHU) DRAWN 4X AND 8X SUPER-IMPOSED UPON ITSELF USING ROTATION
This humble Magic Square of 3x3, rotated upon itself 4 times or at angles of 4x45°gives the pattern on the left, which has become the Logo or Psychic Emblem of EarthHeart School, MiniVersity.
This humble Magic Square of 3x3, rotated upon itself 8 times or at angles of 8x22.5°gives the pattern on the left.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 44 http://www.jainmathemagics.com/product/74/default.asp. Book $50 and eBook $33
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 45
Starr 108 Prana, aged 2 yo, constructing her first Magic Square of 3x3, using String Art, at Durrumbul Hall, far north NSW, 2009.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 46
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 47
LESSON 5 ~ PENTAGRAMS ~ DRAWING FREE-HAND THE UNI-CURSAL PENTAGRAM (WITHOUT TAKING YOUR PEN OFF PAPER) + EMBEDDING THE STAR PENTAGRAM WITHIN ITSELF
Lesson 5 Synopsis or Summary of the Lesson
1 – Drawing Pentacle with a ruler by tracing over dots.
2 – Distinguish between Pentagon and Pentagram.
3 – Drawing Uni-Cursal Pentagram Free-Hand.
4 – Examples of Pentacles in Nature.
5 – Bring to class some apples and pawpaw and cut them transversely to reveal the hidden pentacle seed arrangement.
6 – Drawing the Pentacle within the inner Pentagon 3 times. “Fractal Pent” when “the Inside is the same as the Outside”. Observe how the Pentacle inverts or reverses itself then turns upright again!
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 48
Neatly Draw the Star Pentagram or Pentacle, using a Ruler. You can also draw the Pentagon which are the 5 outer sides joined.
“Uni-Cursal”, is the old Latin or Roman word for “One-Line”
We are the Pentacle!
Did you know that every protein in our human body cells, is in the shape of the Pentacle!
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 49
Practice below, as many free-hand Uni-Cursal 5 pointed-stars as you can, With your Right Hand, without taking your pen or pencil off the paper. Draw the last row of Pentacles with your other or Left hand. On the last page of this Chapter, draw this Uni-Cursal Pentacle freehand, using no dots.
Pentacle May Day Procession, Madrid, 1936
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 50 Here are more examples of Pentacles, some are found in Nature:
Saravanan Thangaraja’s daughter: of Kuala Lumpur,
showing the Perfect Pent Perfection of Papaya (Pawpaw).
Jain 108 Lectures For Children and Adults in 2005
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 51
Here are another 5 examples of the appearance of the Pent shape in Nature
The packing of bubbles displays pent and hex shapes, same as tortoise shell!
The Tomato Leaf is Pent.
(Photo on right is by Jain 108).
The back of the lettuce is a pentacle.
The black sapote “chocolate pudding” fruit has a pentacle design.
Pent in extinct starfish, taken from the classic book: (Photo by Jain 108). “Art Forms In Nature by Ernst Haeckel
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 52
Draw the Pentacle or 5 Pointed Star within itself 2 more times, so that it is first inverted or drawn upside-down, then corrects itself to be upright again, but smaller or miniature in size.
EMBEDDING THE PENTACLE WITHIN ITSELF. THIS IS CALLED FRACTAL. “FRACTAL PENT”
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 53
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 54
LESSON 6 ~ HEXAGRAMS ~ STAR OF DAVID HEXAGRAM + DRAWING FREE-HAND THE UNI-CURSAL HEXAGRAM (WITHOUT TAKING YOUR PEN OFF PAPER)
Lesson 6 Synopsis or Summary of the Lesson
1 – Puzzle: How many same-sized coins can be tiled around a central coin? Trace over the faint lines: “The 6 Around The One”
2 – Examples of The 6 Around The One
3 – Upon 6 dots on a circle, draw both the Hexagon (boundary) and the Hexagram (star pattern)
4 – Trace over the faint lines: “The Star of David” + study the examples of the Star of David
5 – Discuss the Hexagonal Pattern of Bees
6 – Practice drawing freehand the Uni-Cursal Hexagrams (without taking your pen off the paper, like we did with the Pentagram)
7 – Drawing neatly the Uni-Cursal Hexagram (9 attempts)
8 – Drawing neatly the Mystic Rose (Circle of 12 Dots), connecting each of the 12 dots, one to another to make an exquisite pattern
8 – More images of the 12-sided Dodecagon and Dodecagram
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 55 In this lesson, we will draw the Star of David, upon a Circle of 6 Dots, and also the Mystic Rose, based on a Circle with 12 Dots.
Pose the Puzzle: How man circles or coins, of the same size, can be tiled around a central coin?
6 Same Sized Coins can be placed Can you trace over these circles to copy around a central coin the diagram on the left.
Or, you could draw the above diagram of 7 same-sized circles, by tracing a 20 cent coin. Can you draw this diagram without tracing the diagram. Practice this exercise on any piece of paper. This diagram can be called “The Six Around The One” and expresses the number “7”. Place a dot in the centre of each of the 6 outer coins. Proceed to draw an upward-pointing triangle and then a downward-pointing triangle.
More Examples of The 6 Around The 1
Metatron’s Cube Star Tetrahedron Isolated from Metatron’s Cube
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 56
Place a dot in the centre of the 6 Outer Circles, and draw a hexagon (the Hexagon is the boundary of 6 outer sides, whilst the Hexagram is the 2 triangular patterns. Have Child Draw the MYSTIC HEXAGON, means that each dot is drawn to every other dot.
When drawing this, teach them the word “Diameter” (Latin: dia = across)
Solution: Draw over the 2 faint Triangles to create the Star of David, using 2 colours.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 57
When they have done this, they can choose two colours and highlight the two large triangles: to form the Star of David.
More Examples of the Star of David
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 58
Discuss the Hexagonal Pattern of Bees. Perfect Packing. Nature’s Choice. Efficient. Maximum volume for Storing.
On the back cover of this booklet: Can you see the Stars of Davids in this Islamic Pattern? Shade them in?
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 59
PART 2: The UNICURSAL HEXAGRAM Puzzle: Without taking your pen off the paper, in the same way that you previously drew the 5 Pointed-Star without lifting your pen off the page, can you connect these 6 equally spaced dots on the circle, so that all 6 dots are joined. You can only visit each dot once. You must return to the dot that you started on.
Practice below, as many free-hand Uni-Cursal Hexagrams or One-Lined 6-pointed stars, as you can, without taking your pen or pencil off the paper.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 60 Once you have confidently learnt how to draw this, you can draw it again neatly with a ruler.
Neatly Draw the Uni-Cursal Hexagram, using a Ruler.
“Uni-Cursal”, is the old Latin or Roman word for “One-Line”
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 61
Solution
Can you see that all the lines of the Uni-Cursal hexagram
are contained with this drawing of the Cube!
PART 3: The MYSTIC ROSE
(Draw a line from each of the 12 Dots in the Circle, to touch every other Dot in the Circle). Einstein said that there exists a Unified Field, that everything in Space and Time is inter- connected. We can express this geometrically by joining each dot in the circle to every other dot in the circle. So far, we have journeyed with different polygons, progressing from 3 (Triangle) to 4 (Square) to 5 (Pentagon) to 6 (hexagon), skipping 7, 8, 9, 10, 11, and jumping straight to a 12 sided shape. Its name is the Dodecagon. (“Do” means 2 and “Dec means “10”, thus “Dodeca” means 2+10=12. “Gon” means side or edge).
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 62
The Mystic Rose
Solution.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 63 Here are some more images of the 12-sided Dodecagon
3 Squares 4 Triangles
Dodecagram is the 12- Pointed star Pizza of 12 slices. 2 Overlapping Hexagons
12 sided - Pagoda Tiling or Tessellating with an outdoor structure Dodecagons, Hexagons and Squares Contemporary Pop-Art
The Australian 50 cent coin Circle of 12 Squares The Musical Circle of Fifths, 12 notes. Is Dodecahedral
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 64 Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 65
LESSON 7 ~ CUBE COMBINATIONS ~ EXPLORING WOODEN CUBELETS OR SQUARE TILES: NUMBER PATTERNS OR PERMUTATIONS
Lesson 7 Synopsis or Summary of the Lesson
1 – Use house tiles (large ceramic squares) to demonstrate how 2 tiles can be rearranged, face to face only 1 way. + Explain how mirroring works, that the vertical line of 2 tiles is still the same as 2 tiles in the horizontal plane.
2 – Use house tiles (large ceramic squares) to demonstrate how 3 tiles can be rearranged, face to face, no mirrorings. When they learn that there are only 2 combinations or shapes or patterns, they enter that number into their chart. There are 2 pages of square grid paper which is the space for their explorations
3 – Similarly, explore how many original patterns can be made using only 4 tiles
4 – Explore how many original patterns can be made using only 5 tiles
5 – If time permits, explore how many original patterns can be made using only 6 tiles
6 – Bring to the class the excellent tile game called “Tetris” suitable also for adults
ANNOUNCEMENT for Next Lesson on String Art: WHAT TO BRING: – to save you time to Email each parent, remind them now, to bring the following certain items to prepare for the next lesson on String Art: – Lots of various coloured wools of all thicknesses and textures, even some fine cotton string. Fine white thread looks great over layers of darker weavings. – Scissors
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 66 HERE ARE THE RULES: Have a bowlful of wooden blocks, and have your child explore all the possibilities of how they can be tiled, face to face, to make distinctly different variations or permutations. Then count how many permutations are possible. Mirror Images do not count. Faces have to be touching fully, no block can be half way along the face of another block. (In the world of maths and banking and the important Theory of Probabilities, this subject is called COMBINATORICS).
On the following page, each little square is really a wooden cubic block. The technical name for each little cube is “Cubelet” (as in “Piglet” being a small pig). You can put this data into a table:
Number of Blocks Number of Different Permutations
1 1
2 1
3 2
4 5
5 12
6 35
The next 2 pages are the graph paper upon which you can sketch all possible patterns or permutations, followed by the sketched solutions used to calculate this information. Get the child to draw all these squares, by shading them in, and keep exploring. In all these explorations, no Rotations or Mirrorings are allowed, as shown in this diagram on the left. That is, these 8 L-shaped diagrams of 4 tiled squares are considered to be only 1 shape.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 67
On this Graph Paper, can you explore all the possible patterns for 4 Cubes, and also 5 cubes. Best to do this with lead pencil first, then outline the correct patterns in pen, and if you choose, colour them in. How many Permutations are there?
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 68
On this Graph Paper, can you explore all the possible patterns for 6 Cubes. Best to do this with lead pencil first, then outline the correct patterns in pen, and if you choose, colour them in. How many Permutations are there?
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 69
Cube Permutations: Solutions
The cube permutations using only 1, 2, 3 or 4 Squares or Cubic Blocks nb: 3 Tiles have 3 Permutations and 4 Tiles have 5 Permutations
The 12 possible cube permutations using only 5 Squares or Cubic Blocks
The 35 possible cube permutations using only 6 Squares or Cubic Blocks
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 70 Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 71
LESSON 8 ~ STRING ART ~
Lesson 8 Synopsis or Summary of the Lesson
1 – Instead of using nails on a wooden board, the Teacher is to pre-make circular cardboard cut-outs, the size of a plate, or the size that your protractor will allow to fit a standard page (refer to the first image seen in this chapter). I use a large plastic protractor whose diameter is just over 224 mm. – On the large square cardboard, draw 2 circles in pen or pencil, the larger one (diameter 224 mm) is to be cut out by the child or assisting parent, and the inner one (diameter 150 mm). – Draw 12 straight lines that join only the 2 circles (not going right through the circle) as these 12 short lines will be the slit marks that the child or parent will cut with their scissors. The 12 slit marks need to be cut very precisely otherwise the final pattern may not look symmetrical.
2 – Each child will be given one of these cardboard discs
3 – The teacher can supply and bring their own large wooden circular board with either 12 or 24 nails and have some children come up and explore some of the basic shapes like triangle, square, hexagon and octagon and dodecagon. But on this Wheel of 12 or 24 nails, they cannot make the Pentagon or Decagon, so also have another large wooden circular board with 10 nails to explain this.
4 – Show other examples of String Art and String Sculpture
WHAT TO BRING: – Email each parent, or tell them the week before, to bring the following certain items to prepare for this lesson: – Lots of various coloured wools of all thicknesses and textures, even some fine cotton string. Fine white thread looks great over layers of darker weavings. – Scissors
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 72 Ideally, we would want to use nails hammered into wooden boards, the concept being that the Parent assists the young child in forming the carpentry required, with the Child observing how the Parent forms the templates or grids or masters for the pattern selected. Given in this chapter are other options besides using nails on board.
Cardboard Cut-outs, using slits instead of nails
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 73
STRING ART – THREAD ART TEMPLATES: OPTIONAL or can be done at Home
Circular design with 21 points Hexagon with 11 nails per edge.
Star Hexagon with 12 nails Square Design with 25 nails per edge. per radius along 3 main axes.
L-Shaped Design with 12 nails per edge. These two axes are 90 degrees apart, also called perpendicular or orthogonal. Cross Design with 12 nails per arm.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 74
Other Inspirational Examples of String Art, using Nails and Wooden Board for Resource or Creative Ideas
This 16 pointed star, on the right hand side, can be drawn 5 times, in 5 different colours. This means that you would have to create a circle with 16x5=80 nails. Dividing this into 360 degrees gives a spacing of 4.5 degrees for each nail.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 75
Other Examples of String Art, not using Nail and Board, for Inspirational Resource or Creative Ideas
Online Toys Australia, has cut-out edges, with no nails. Using punched holes Using a metal ring Observe the edges and how into the cardboard they have been cut out. is a clever idea. or hoop.
Cutting out a flower design with petals Using string art directly and overlapping with string art. Letters of the Alphabet. on a wall!
Using String Art in Space, has the qualities of an installation or a sculptural art piece.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 76
Picture of Starzi Porter, at 8 years of age, holding a circular piece of String Art that she spontaneously weaved upon a breadboard with 12 nails, in October 2014 in Mullumbimby when we covered 9 weeks of After-School classes.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 77 Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 78
LESSON 9 ~ CREATION OF THE 7-CIRCUIT LABYRINTH ~
Lesson 9 Synopsis or Summary of the Lesson
1 –Practice drawing freehand a 5x5 Grid of Dots based on drawing a 4x4 Grid of Squares to create a periphery or boundary of 16 dots around a square. Practice drawing the central cross and the 4 angular “L”s to begin drawing the labyrinth
2 – Have students come on the whiteboard or blackboard practicing this grid
3 – Introduce the rules of how to draw the subsequent curves, starting from zenith, moving from left to right
4 – Explain how this is similar but not identical to the labyrinth in Chartres cathedral which is an 11-circuit labyrinth, but can be drawn the same way
5 – Have children draw this on the whiteboard, giving them the grid only and getting them to do all the curves neatly.
6 – Observe that there is only one entry point or doorway into the labyrinth. What is the symbolism of this Journey, how we end up in the centre, then retrace our steps to get back out again.
7 – Explain the difference between a Maze and a Labyrinth; a maze is designed to get you lost, where a Labyrinth is designed to take you to the centre or the heart of a system
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 79 This page or chapter or worksheet can be used at any time during the 9 Lessons / 9 Week course. It is a very special “fill-in” in the event a class finishes early. It may look like a very difficult pattern to construct, but it is actually very easy to construct, and parents are very amazed that their 5 or 6 yo child could draw this series of curves to construct such a highly intelligent and sophisticated design. So we begin with a 5x5 grid of dots, insert a few axes of symmetry in the form of a cross, and follow the instructions to merely draw curves in a clockwise direction, starting from the topmost north or zenith point.
Explain to the child the difference between a Maze and a Labyrinth. A Maze is a designed to get you lost! A Labyrinth is a Journey that takes you to the Centre of Creation, and the Path back home is a retracing of the same steps that took you in.
This 7-circuit Labyrinth, will be explained further in the booklet for Mathemagics For Juniors, as the actual 5x5 grid and cross-like axes are based on the highlighting of all the odd numbers within the Magic Square of 9x9 that the students actually create from scratch, beginning from 1 to 2 to 3 to the last number 81 (an image of this shown on the next page).
An understanding of how to create this 7-circuit Labyrinth, will teach the Child how to draw the 11-Circuit Labyrinth which is made in stone in Chartres Cathedral, France, around the year 1,200 AD. This is Sacred Geometry at its best, and can be taught to the Child in a simple and elegant way. At first sight, you would think that a child under 10 yo could not possibly construct this!
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 80
How To Create The 7-Circuit Labyrinth, the basis of stone-floor labyrinth in Chartres Cathedral
7-Circuit Labyrinth drawn by the Child and the 11-Circuit Labyrinth on the stone floor of the Chartres Cathedral.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 81 Practice drawing your own 7-Circuit Laybrinth, freehand. Start at the Zenith.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 82
Here is another unusual 7-circuit labyrinth, where the centre is a tree! It also has a different walking pattern.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 83
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 84 PROMOTIONAL PROSTERS
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 85
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 86
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 87
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 88
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 89
BACK COVER BLURB Mathemagics For Starkidz
Get involved with your Child’s education. This highly visual curriculum for Children aged from 5 to 8 is the first of its kind, introducing young children to the fascinating world of Sacred Geometry and Mandala Creation. Mathemagics For Starkidz is a highly visual presentation of the ancient branch of mathematics called Sacred Geometry. It is encouraged that these Starkidz learn these 9 lessons as a precursor to learning their Multiplication Table which is recommended for 9 to 12 year olds (Mathemagics For Juniors). When the Numbers (Male Left Brain) of a Magic Square are translated into a Picture, it creates Whole Brain Learning or Feminine Right Brain Mathematics that responds to pictures. This course teaches the Beauty of Mathematics and Geometry. A lot of this material was in the original Greek syllabus 2000 years ago and it got taken out about 100 years ago. Jain is merely putting back into the curriculum that which was always there. Jain talks to the children as if they were young adults, using a highly intelligent vocabulary of words like Torus, Fractal, Platonic Solids, Labyrinth all of which they understand.
The contents include: • Drawing Circles + Weaving Semi-Circles Free-Hand • Triangle Numbers + Tetrahedron Numbers • Square Numbers + Cube Numbers (Cubic Number Patterns) • The Magic Square of 3x3 Lo-Shu Pattern + Rotating it upon itself at a 90 Degree Rotation • Pentagrams. Drawing Freehand the Uni-Cursal Pentagram + Embedding the Pentacle Within Itself • Hexagrams + The Star of David + Drawing Free-hand the Uni-Cursal Hexagram (Without Taking Your Pen Off The Paper) + Mystic Rose • Cube Combinations + Exploring Wooden Cubelets or Square Tiles: Number Patterns or Permutations. • String Art • Creation of the 7-Circuit Labyrinth
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 90
Picture of Amala Aylward, at 8 years of age, holding a sketching of some of the 5 Platonic Solids that she drew in October 2014 in Mullumbimby when we covered 4 weeks of After-School classes.
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 91
Lila Boddington drawing a Magic Square of 4x4
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 92
Yasmin Tay of Singapore drawing a Fractal Pentacle, July 2015
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 93
Eric & Amalia Borg-Olivier, 2015
Mathemagics For StarKidz, by Jain 108 Term 1 of 2015 For Ages 5 to 8 page 94 MATHEMAGICSFORSTAR-KIDZ WORKBOOK Get involved with you Child’s educa on. This highly visual curriculum for Children aged from 5 to 8 is the first of its kind, introducing young children to the facina ng world of Sacred Geometry and Mandala Crea on. MathemagicsM For Starkidz is a highly visual presenta on of the ancient branch of mathema cs called Sacred Geometry. It is encouraged that these Starkidz learn these 9 lessons as a precursor to learning their Mul plica on Table which is recommended for 9 to 12 year olds (Mathemagics For Juniors). When the Numbers (Male Le Brain) of a Magic Square are translated into Art, it creates Whole Brain Learning or Feminine Right Brain Mathema cs that responds to Pictures. This course teaches the Beauty of Mathema cs and Geometry. A lot of this material was in the original Greek syllabus 2000 years ago and it got taken out about 100 years ago. Jain is merely pu ng back into the curriculum that which was always there. Jain talks to the children as if they were young adults, using a highly intelligent vocabulary of words like Torus, Fractal, Platonic Solids, Labyrinth all of which they understand. The contents include:
• Drawing Circles + Weaving Semi-Circles Free-Hand • Triangle Numbers + Tetrahedron Numbers • Square Numbers + Cube Numbers (Cubic Number Pa erns) • The Magic Square of 3x3 Lo-Shu Pa ern + Rota ng it upon itself at a 90 Degree Rota on • Pentagrams. Drawing Freehand the Uni-Cursal Pentagram + Embedding the Pentacle Within Itself • Hexagrams + The Star of David + Drawing Free-hand the Uni-Cursal Hexagram (Without Taking Your Pen Off The Paper) + Mys c Rose • Cube Combina ons + Exploring Wooden Cubelets or Square Tiles: Number Pa erns or Permuta ons. • String Art • Crea on of the 7-Circuit Labyrinth (progression shown below in 3 steps)
jainmathemagics.com
PUBLISHED2015