Similarity- Similarity occurs when an object is the same as another object except in a different scale (size) then the original. In triangles, two are only similar if they have all the same angles or their sides are proportional to each other. Squares are always similar and rectangles must have proportional sides as well.
Gnomons- A gnomon in math terms is an object G that fits together with another object A but remains similar to object A just on a different scale.
Disks and Circles are Always similar under every circumstance. A circle could only be an object A but never a gnomon because of its properties.
Circular Rings would be the object A and the gnomon would be the other shape but it does have a gnomon. The shapes of the inner and outer radii however have to be proportional or it is not similar.
Rectangles can be the object A but not the gnomon and only if the gnomon that fits on to it has sides corresponding to that of the rectangle being used for object A.
Circular Disks The O shaped ring would be the gnomon to the smaller filled in circle and that circles diameter would have to also be proportional to the gnomons thickness.
Squares once again the square must be the Object A and the L shaped figure would have to be the proportional gnomon.
Triangles Object A and the gnomon can be any type of triangle as long as it ends up having the same angle sizes or side lengths as triangle object A
Note: A rectangle can not be its on gnomon because you cant separate a rectangle from a rectangle without leaving an L shaped figure behind and that L shaped figure would not be proportional to the rectangle that object A and the gnomon would form when combined together.
The Golden Rectangle is the special rectangle that is just the perfect balance between being too skinny and too squarish that appeals most naturally to us as humans in nature and occurs in all of our modern appliances and objects in our world. It is...