By Denton, Desmond & Acqeel Federation Square Verify that for a triangle with rational angles will have rotational symmetry if rotated by one of its internal angles (Question C) Bibliography (Question B) Why does not rotational symmetry apply for the Golden Triangle? http://en.wikipedia.org/wiki/File:Pinwheel_2.gif Yellow = x

Red = 1

Green = x - 1 With the Golden Rectangle you have measurements of x * 1, you want to get a square out of x * 1, To do that you put a 1 through the rectangle to get a square ( 1 squared) this leaves you a little rectangle (1 * (x - 1)). We want to keep the ratio the same, so you get; (x : 1 = 1 : x - 1) The ratio keeps going. the number summed up is phi / = Figure 2.0: The shape of a "super triangle" (golden triangle compilation) when completed. Created on GeoGebra Creating a Super Triangle Step 1 Figure 2.3: Single Golden Triangle

Total Length: 5 units

Total Height: 2 units Creating a Super Triangle Step 2 Figure 2.1: Initial Triangle

Base length - 2 units

Height - 1 unit Angles: 90°, 60°, 30° Figure 2.2: The "initial triangle" is a Golden Triangle in itself! Creating a Super Triangle Step 5 Creating a Super Triangle Step 3 Creating a Super Triangle Step 4 Figure 2.4: Rotation Figure 2.5: Rotation Figure 2.6: Rotation Creating a Super Triangle Step 6 Figure 2.7: Rotation The Super Triangle A compilation of infinitive Golden Triangles Yet with no rotational symmetry... Figure 2.9: The "pinwheel" process Figure 2.0: A Super Triangle or a Super Super triangle. There is no definitive way of knowing exactly what it is called. Rotational Symmetry This is the result of the triangle being rotated around the point A 16 times.

360 divided by 30 = 12 Right Angled triangle with angles 30 and 60 Rotational Symmetry This is the result of the triangle

being rotated around the middle point 4 times. 360 divided by 90 is 4. Rotational Symmetry This is the result of the triangle being rotated around the point C 6 times, 360 divided by 60= 6 http://www.qedcat.com/archive/129.html

http://www.qedcat.com/archive/federation.html

http://mathworld.wolfram.com/GoldenRatio.html

Resources: GeoGebra, Prezi

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# Maths Fed Square

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