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# MATHS SPIROGRAPHS

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## Rachael Sung

on 29 November 2012

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#### Transcript of MATHS SPIROGRAPHS

SPIROGRAPHS WEIRD? IMAGINE GETTING A SET OF CIRCLES
FOR YOUR BIRTHDAY... A spirograph is a geometric drawing toy that was developed by British engineer Denys Fisher.
Traditionally the set of small wheels had teeth along their rims and each wheel had small holes in various places where the pen would be positioned.
Inserting the pen in one of the holes, you would move the wheel around the ring, and create mathematical curves and patterns WHAT IS A SPIROGRAPH? Although they may sound technical;
a hypocycloid is created when the wheel moved inside the rim of the ring (HYPO= under)
an epicycloid is created when the wheel moved outside the rim of the ring. (EPI= over) HYPOCYCLOIDS AND EPICYCLOIDS OBSERVATION 1 If radius a and b is same, and if the pen is at the centre of the revolving circle than it creates a perfect circle.
When the radius of both are equal (r1=r2) and pen is actually on the moving circle it creates a cardiord and has one cusp. OBSERVATION 3 When radius B is smaller than radius A, and the pen position is same as radius B it creates a star inside the circle. OBSERVATION 2 If the radius B of the circle is smaller than radius A and is inside it, the pattern becomes a triangle.
If radius A and B are equal, but the pen position is different, a circle will be created but it won't be concentric. ADDITIONAL OBSERVATIONS When r1=1/2 r2, it creates a nephroid, and has 2 cusps. As a general rule, the smaller ratio, the more cusps and the more interesting the design is. visit mathplayground.com/Spirograph.html
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