Spiraling Squares

Spiraling Squares Pretty. And interesting, we think. Do you see a lot of spirals in this image? 1. Carefully add to this picture as many spiraling arcs that you can discern. I made this shape by starting in the middle. I placed 12 squares in a circle evenly spaced. 2. What would be the central angle that surrounds each square? Let's just say that those first squares had side 1 cm. The next round of squares had sides that were the same size as the diagonal of the first square. 3. Using the Pythagorean theorem, what size are the sides of those next squares in the second round? 4. Continue to calculate the sides of the squares in this pattern. I drew some golden lines along the sides of some of the squares. The golden lines seem to make a lovely arc. 5. What can you figure out about those arcs? Wikipedia lists many sorts of spirals and their general forms: Archimedean spiral � = � + � ∗ � Euler spiral Curvature of curve = reciprocal of radius ! Fermat's spiral � = � ! ! Hyperbolic spiral � = ! Logarithmic spiral � = � ∗ � !∗! And more ... 6. Make a guess about which sort of spiral the spiraling squares design is most like and explain your thoughts. If you would like to create this design on your own, we've given you a starting sheet of polar graph paper already containing 12 little squares arranged in a circle and some instructions. To complete this design you will need a pencil, compass and a straight edge. Sources: https://en.wikipedia.org/wiki/Spiral Mathematical Quilts by Diana Venters and Elaine Krajenke Ellison (1999) Key Curriculum Press Brought to you by YummyMath.com .

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Coverrailway Curves Book.Cdr
RAILWAY CURVES March 2010 (Corrected & Reprinted : November 2018) INDIAN RAILWAYS INSTITUTE OF CIVIL ENGINEERING PUNE - 411 001 i ii Foreword to the corrected and updated version The book on Railway Curves was originally published in March 2010 by Shri V B Sood, the then professor, IRICEN and reprinted in September 2013. The book has been again now corrected and updated as per latest correction slips on various provisions of IRPWM and IRTMM by Shri V B Sood, Chief General Manager (Civil) IRSDC, Delhi, Shri R K Bajpai, Sr Professor, Track-2, and Shri Anil Choudhary, Sr Professor, Track, IRICEN. I hope that the book will be found useful by the field engineers involved in laying and maintenance of curves. Pune Ajay Goyal November 2018 Director IRICEN, Pune iii PREFACE In an attempt to reach out to all the railway engineers including supervisors, IRICEN has been endeavouring to bring out technical books and monograms. This book “Railway Curves” is an attempt in that direction. The earlier two books on this subject, viz. “Speed on Curves” and “Improving Running on Curves” were very well received and several editions of the same have been published. The “Railway Curves” compiles updated material of the above two publications and additional new topics on Setting out of Curves, Computer Program for Realignment of Curves, Curves with Obligatory Points and Turnouts on Curves, with several solved examples to make the book much more useful to the field and design engineer. It is hoped that all the P.way men will find this book a useful source of design, laying out, maintenance, upgradation of the railway curves and tackling various problems of general and specific nature.
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ALL ABOUT SPIRALS a Spiral Can Be Described As Any 2D Continuous Curve Where the Radial Distance R from the Origin Equals a Specified Function of the Angle Θ
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Leeds Thesis Template
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