Design of Hexadecagon Circular Patch Antenna with DGS at Ku Band for Satellite Communications
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Islamic Geometric Ornaments in Istanbul
►SKETCH 2 CONSTRUCTIONS OF REGULAR POLYGONS Regular polygons are the base elements for constructing the majority of Islamic geometric ornaments. Of course, in Islamic art there are geometric ornaments that may have different genesis, but those that can be created from regular polygons are the most frequently seen in Istanbul. We can also notice that many of the Islamic geometric ornaments can be recreated using rectangular grids like the ornament in our first example. Sometimes methods using rectangular grids are much simpler than those based or regular polygons. Therefore, we should not omit these methods. However, because methods for constructing geometric ornaments based on regular polygons are the most popular, we will spend relatively more time explor- ing them. Before, we start developing some concrete constructions it would be worthwhile to look into a few issues of a general nature. As we have no- ticed while developing construction of the ornament from the floor in the Sultan Ahmed Mosque, these constructions are not always simple, and in order to create them we need some knowledge of elementary geometry. On the other hand, computer programs for geometry or for computer graphics can give us a number of simpler ways to develop geometric fig- ures. Some of them may not require any knowledge of geometry. For ex- ample, we can create a regular polygon with any number of sides by rotat- ing a point around another point by using rotations 360/n degrees. This is a very simple task if we use a computer program and the only knowledge of geometry we need here is that the full angle is 360 degrees. -
Polygon Review and Puzzlers in the Above, Those Are Names to the Polygons: Fill in the Blank Parts. Names: Number of Sides
Polygon review and puzzlers ÆReview to the classification of polygons: Is it a Polygon? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon Not a Polygon Not a Polygon (straight sides) (has a curve) (open, not closed) Regular polygons have equal length sides and equal interior angles. Polygons are named according to their number of sides. Name of Degree of Degree of triangle total angles regular angles Triangle 180 60 In the above, those are names to the polygons: Quadrilateral 360 90 fill in the blank parts. Pentagon Hexagon Heptagon 900 129 Names: number of sides: Octagon Nonagon hendecagon, 11 dodecagon, _____________ Decagon 1440 144 tetradecagon, 13 hexadecagon, 15 Do you see a pattern in the calculation of the heptadecagon, _____________ total degree of angles of the polygon? octadecagon, _____________ --- (n -2) x 180° enneadecagon, _____________ icosagon 20 pentadecagon, _____________ These summation of angles rules, also apply to the irregular polygons, try it out yourself !!! A point where two or more straight lines meet. Corner. Example: a corner of a polygon (2D) or of a polyhedron (3D) as shown. The plural of vertex is "vertices” Test them out yourself, by drawing diagonals on the polygons. Here are some fun polygon riddles; could you come up with the answer? Geometry polygon riddles I: My first is in shape and also in space; My second is in line and also in place; My third is in point and also in line; My fourth in operation but not in sign; My fifth is in angle but not in degree; My sixth is in glide but not symmetry; Geometry polygon riddles II: I am a polygon all my angles have the same measure all my five sides have the same measure, what general shape am I? Geometry polygon riddles III: I am a polygon. -
Formulas Involving Polygons - Lesson 7-3
you are here > Class Notes – Chapter 7 – Lesson 7-3 Formulas Involving Polygons - Lesson 7-3 Here’s today’s warmup…don’t forget to “phone home!” B Given: BD bisects ∠PBQ PD ⊥ PB QD ⊥ QB M Prove: BD is ⊥ bis. of PQ P Q D Statements Reasons Honors Geometry Notes Today, we started by learning how polygons are classified by their number of sides...you should already know a lot of these - just make sure to memorize the ones you don't know!! Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon 12 Dodecagon 13 Tridecagon 14 Tetradecagon 15 Pentadecagon 16 Hexadecagon 17 Heptadecagon 18 Octadecagon 19 Enneadecagon 20 Icosagon n n-gon Baroody Page 2 of 6 Honors Geometry Notes Next, let’s look at the diagonals of polygons with different numbers of sides. By drawing as many diagonals as we could from one diagonal, you should be able to see a pattern...we can make n-2 triangles in a n-sided polygon. Given this information and the fact that the sum of the interior angles of a polygon is 180°, we can come up with a theorem that helps us to figure out the sum of the measures of the interior angles of any n-sided polygon! Baroody Page 3 of 6 Honors Geometry Notes Next, let’s look at exterior angles in a polygon. First, consider the exterior angles of a pentagon as shown below: Note that the sum of the exterior angles is 360°. -
Geometrygeometry
Park Forest Math Team Meet #3 GeometryGeometry Self-study Packet Problem Categories for this Meet: 1. Mystery: Problem solving 2. Geometry: Angle measures in plane figures including supplements and complements 3. Number Theory: Divisibility rules, factors, primes, composites 4. Arithmetic: Order of operations; mean, median, mode; rounding; statistics 5. Algebra: Simplifying and evaluating expressions; solving equations with 1 unknown including identities Important Information you need to know about GEOMETRY… Properties of Polygons, Pythagorean Theorem Formulas for Polygons where n means the number of sides: • Exterior Angle Measurement of a Regular Polygon: 360÷n • Sum of Interior Angles: 180(n – 2) • Interior Angle Measurement of a regular polygon: • An interior angle and an exterior angle of a regular polygon always add up to 180° Interior angle Exterior angle Diagonals of a Polygon where n stands for the number of vertices (which is equal to the number of sides): • • A diagonal is a segment that connects one vertex of a polygon to another vertex that is not directly next to it. The dashed lines represent some of the diagonals of this pentagon. Pythagorean Theorem • a2 + b2 = c2 • a and b are the legs of the triangle and c is the hypotenuse (the side opposite the right angle) c a b • Common Right triangles are ones with sides 3, 4, 5, with sides 5, 12, 13, with sides 7, 24, 25, and multiples thereof—Memorize these! Category 2 50th anniversary edition Geometry 26 Y Meet #3 - January, 2014 W 1) How many cm long is segment 6 XY ? All measurements are in centimeters (cm). -
Polygon Rafter Tables Using a Steel Framing Square
Roof Framing Geometry & Trigonometry for Polygons section view inscribed circle plan view plan angle polygon side length central angle working angle polygon center exterior angle radius apothem common rafter run plan view angle B hip rafter run angle A roof surface projection B Fig. 50 projection A circumscribed circle Polygons in Mathematical Context Polygons in Carpenters Mathematical Context central angle = (pi × 2) ÷ N central angle = 360 ÷ N working angle = (pi × 2) ÷ (N * 2) working angle = 360 ÷ (N × 2) plan angle = (pi - central angle) ÷ 2 plan angle = (180 - central angle) ÷ 2 exterior angle = plan angle × 2 exterior angle = plan angle × 2 projection angle A = 360 ÷ N S is the length of any side of the polygon projection angle B = 90 - projection angle a N is the number of sides R is the Radius of the circumscribed circle apothem = R × cos ( 180 ÷ N ) apothem is the Radius of the inscribed circle Radius = S ÷ ( 2 × sin ( 180 ÷ N )) pi is PI, approximately 3.14159 S = 2 × Radius × sin ( 180 ÷ N ) Projection A = S ÷ cos ( angle A ) pi, in mathematics, is the ratio of the circumference of a circle to Projection B = S ÷ cos ( angle B ) its diameter pi = Circumference ÷ Diameter apothem multipler = sec (( pi × 2 ) ÷ ( N × 2 )) working angle multipler = tan (360 ÷ ( N × 2 )) × 2 apothem = R × cos ( pi ÷ N ) rafter multipler = 1 ÷ cos pitch angle apothem = S ÷ ( 2 × tan (pi ÷ N )) hip multipler = 1 ÷ cos hip angle Radius = S ÷ (2 × sin (pi ÷ N )) rise multipler = 1 ÷ tan pitch angle Radius = 0.5 × S × csc ( pi ÷ N ) S = 2 × Radius × sin ( pi ÷ N ) Hip Rafter Run = Common Rafter Run × apothem multipler S = apothem × ( tan ((( pi × 2 ) ÷ (N × 2 ))) × 2 ) Common Rafter Run = S ÷ working angle multipler S = R × sin ( central angle ÷ 2 ) × 2 S = Common Rafter Run × working angle multipler S = R × sin ( working angle ) × 2 Common Rafter Run = apothem Common Rafter Span = Common Rafter Run × 2 Hip Rafter Run = Radius 1 What Is A Polygon Roof What is a Polygon? A closed plane figure made up of several line segments that are joined together. -
Originality Statement
PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet Surname or Family name: Hosseinabadi First name: Sanaz Other name/s: Abbreviation for degree as given in the University calendar: PhD School: School of Architecture Faculty: Built Environment Title: Residual Meaning in Architectural Geometry: Tracing Spiritual and Religious Origins in Contemporary European Architectural Geometry Abstract 350 words maximum: (PLEASE TYPE) Architects design for more than the instrumental use of a buildings. Geometry is fundamental in architectural design and geometries carry embodied meanings as demonstrated through the long history of discursive uses of geometry in design. The meanings embedded in some geometric shapes are spiritual but this dimension of architectural form is largely neglected in architectural theory. This thesis argues that firstly, these spiritual meanings, although seldom recognised, are important to architectural theory because they add a meaningful dimension to practice and production in the field; they generate inspiration, awareness, and creativity in design. Secondly it will also show that today’s architects subconsciously use inherited geometric patterns without understanding their spiritual origins. The hypothesis was tested in two ways: 1) A scholarly analysis was made of a number of case studies of buildings drawn from different eras and regions. The sampled buildings were selected on the basis of the significance of their geometrical composition, representational symbolism of embedded meaning, and historical importance. The analysis clearly traces the transformation, adaptation or representation of a particular geometrical form, or the meaning attached to it, from its historical precedents to today. 2) A scholarly analysis was also made of a selection of written theoretical works that describe the design process of selected architects. -
Regular Polygon Square
American Journal of Mathematics and Statistics 2017, 7(1): 32-37 DOI: 10.5923/j.ajms.20170701.05 A General Method of Constructing Polygons from a Square Ohochuku N. Stephen Department of Chemistry, Ignatius Ajuru University of Education, Port Harcourt, Nigeria Abstract This paper presents a method for constructing any regular polygon from a square of same side length. The method uses the diagonal of the square to determine the radius of a circle that is equally sectored using the side of the square. The equal sector chords form the sides of the required regular polygon. The method can be applied in the construction of any regular polygon angle (and many other angles) and in inscribing regular polygon in a given circle. The method and its applications are simple, easy to manipulate and requires no construction of angles except 90o for the construction of the nuclear figure the square. Keywords Regular polygon square As mentioned above, majority of the methods of 1. Introduction constructing regular polygons are tailored to particular family. A regular polygon family consists of regular A regular polygon is any geometric plane figure bound by polygons that differ in side lengths only. A question arises three or more equal straight lines and possessing equal whether there can be a general method that is applicable to internal angles [1, 2]. Plane figures as the equilateral the construction of any of the polygon family? The answer is triangles, squares, pentagons, hexagons etc are the lower yes because there is a method describing the construction of families. The constructions of regular polygons demands regular polygons on same base [6] which is termed the “two special methods because the majority of their respective base triangle rule”. -
Arithmetica Logarithmica Chapter Twenty Eight. [P.78.] Synopsis
Arithmetica Logarithmica 28 - 1 §28.1. Synopsis: Chapter Twenty - Eight. The Lemma below is stated, relating the proportionality between the areas of inscribed and circumscribed regular figures, of a given order for a given circle, to the area of the inscribed figure with double the sides, and demonstrated with a number of examples: (i) The inscribed regular hexagon has an area which is the mean proportional between the areas of the inscribed and circumscribed equilateral triangles; similarly, for the cases: (ii) the regular inscribed/circumscribed hexagons with the regular inscribed dodecagon ; (iii) the regular inscribed/circumscribed squares with the regular inscribed octagon; (iv) the regular inscribed/circumscribed pentagons with the regular inscribed decagon. [If an is the area of the inscribed n-gon, and An the area of the circumscribed n-gon, for a given circle, then a2n = √(an.An).] A large list of calculated lengths of side for inscribed/circumscribed regular figures in a circle with unit radius is presented, together with their perimeters and areas. A number of scaling problems is then demonstrated, showing the great advantage of using logarithms. §28.2. Chapter Twenty Eight. [p.78.] With the diameter of a circle given, to find the sides and areas of the regular Triangle, Square, Pentagon, Hexagon, Octagon, Decagon, Dodecagon, Hexadecagon, inscribed and circumscribed in the same circle. Lemma or regular figures ascribed in a circle: Let two figures of the same kind be associated with Fthe same circle, the one inscribed and the other circumscribed: if a third figure, of which the number of sides is equal to the sum of the remaining sides taken together, is to be inscribed in the same circle , then the area of this figure is the mean proportional between the remaining areas. -
Geometry in Design Geometrical Construction in 3D Forms by Prof
D’source 1 Digital Learning Environment for Design - www.dsource.in Design Course Geometry in Design Geometrical Construction in 3D Forms by Prof. Ravi Mokashi Punekar and Prof. Avinash Shide DoD, IIT Guwahati Source: http://www.dsource.in/course/geometry-design 1. Introduction 2. Golden Ratio 3. Polygon - Classification - 2D 4. Concepts - 3 Dimensional 5. Family of 3 Dimensional 6. References 7. Contact Details D’source 2 Digital Learning Environment for Design - www.dsource.in Design Course Introduction Geometry in Design Geometrical Construction in 3D Forms Geometry is a science that deals with the study of inherent properties of form and space through examining and by understanding relationships of lines, surfaces and solids. These relationships are of several kinds and are seen in Prof. Ravi Mokashi Punekar and forms both natural and man-made. The relationships amongst pure geometric forms possess special properties Prof. Avinash Shide or a certain geometric order by virtue of the inherent configuration of elements that results in various forms DoD, IIT Guwahati of symmetry, proportional systems etc. These configurations have properties that hold irrespective of scale or medium used to express them and can also be arranged in a hierarchy from the totally regular to the amorphous where formal characteristics are lost. The objectives of this course are to study these inherent properties of form and space through understanding relationships of lines, surfaces and solids. This course will enable understanding basic geometric relationships, Source: both 2D and 3D, through a process of exploration and analysis. Concepts are supported with 3Dim visualization http://www.dsource.in/course/geometry-design/in- of models to understand the construction of the family of geometric forms and space interrelationships. -
Examples of Polygons in the Home
Examples Of Polygons In The Home Weider remains chewiest: she result her mahout tumblings too commercially? Scott usually suedes wamblingly or throbs unconstitutionally when unexplainable Rick toggles identically and photoelectrically. Huffing Rab sometimes apportion any evaginations achromatized peacefully. Below to home ranges using these. Have sides of home range will meet all examples of a fraction? Compose them to home range, they have kids quiz. Brick pattern on your operations to the examples polygons of home learning about polygons? Another example is then cut, using a home range of the examples have to a polygon that you. Formed by using protractors. The real life almost at buildings and polygons of in the examples home ranges using their claims add four simple! The third vertex of home range will quickly find the same size, from the value of interesting polygon with the pattern as an unusual traffic. Notice examples of home range will be done by their simplest form pentagonal tilings. We are of polygons the examples in the procedure for one. The length and perimeter and the perimeter is a subset of them to the polygons that i used to back of reflections are thus more. Is there really quadrilateral has the polygon because a home of. Then tracing round flying saucers, in polygons of the examples home range size. How many sides and follow a home range, there are also in each other isosceles. Triangle have students use polygons and minor axes are not the examples of polygons in the distance around the members of. Use of the two types of paper diagonally to google tiles which implies that not create a triangle to be useful, and how polygons together? To fit inside the exterior angle, bridges used in your experience of the boat nowadays have crescent shapes and examples of in polygons the home range will not only the plane with it. -
REALLY BIG NUMBERS Written and Illustrated by Richard Evan Schwartz
MAKING MATH COUNT: Exploring Math through Stories Great stories are a wonderful way to get young people of all ages excited and interested in mathematics. Now, there’s a new annual book prize, Mathical: Books for Kids from Tots to Teens, to recognize the most inspiring math-related fiction and nonfiction books that bring to life the wonder of math in our lives. This guide will help you use this 2015 Mathical award-winning title to inspire curiosity and explore math in daily life with the youth you serve. For more great books and resources, including STEM books and hands-on materials, visit the First Book Marketplace at www.fbmarketplace.org. REALLY BIG NUMBERS written and illustrated by Richard Evan Schwartz Did you know you can cram 20 billion grains of sand into a basketball? Mathematician Richard Evan Schwartz leads readers through the GRADES number system by creating these sorts of visual demonstrations 6-8 and practical comparisons that help us understand how big REALLY WINNER big numbers are. The book begins with small, easily observable numbers before building up to truly gigantic ones. KEY MATH CONCEPTS The Mathical: Books for Kids from Tots to Teens book prize, presented by Really Big Numbers focuses on: the Mathematical Sciences Research • Connecting enormous numbers to daily things familiar to Institute (MSRI) and the Children’s students Book Council (CBC) recognizes the • Estimating and comparing most inspiring math-related fiction and • Having fun playing with numbers and puzzles nonfiction books for young people of all ages. The award winners were selected Making comparisons and breaking large quantities into smaller, by a diverse panel of mathematicians, easily understood components can help students learn in ways they teachers, librarians, early childhood never thought possible. -
Handling Handles. Part II. Stratification and Data Analysis
Handling Handles. Part II. Stratification and Data Analysis T. Bargheera,b,c, J. Caetanod, T. Fleuryd,e, S. Komatsuf , P. Vieirag,h aInstitut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany bDESY Theory Group, DESY Hamburg, Notkestraße 85, D-22603 Hamburg, Germany cKavli Institute for Theoretical Physics, University of California Santa Barbara, CA 93106, USA dLaboratoire de Physique Théorique de l’École Normale Supérieure de Paris, CNRS, ENS & PSL Research University, UPMC & Sorbonne Universités, 75005 Paris, France. eInternational Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario, Lagoa Nova, Natal-RN 59078-970, Brazil f School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA gPerimeter Institute for Theoretical Physics, 31 Caroline St N Waterloo, Ontario N2L 2Y5, Canada hInstituto de Física Teórica, UNESP - Univ. Estadual Paulista, ICTP South American Institute for Fundamental Research, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP, Brasil [email protected], [email protected], [email protected], [email protected], [email protected] Abstract In a previous work [1], we proposed an integrability setup for computing non-planar corrections to correlation functions in N = 4 super Yang– Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over arXiv:1809.09145v2 [hep-th] 4 Jun 2019 graphs can be interpreted as a quantization of the string moduli space integration.