Square to Circle and more

How can we transform a square to a circle, or a circle to a triangle? Is it exist that transformation? Using The Geometer's Sketchpad, we can morph from a triangle to a square to a circle in a quite simple way. First, we create three objects: a square, a circle and a triangle.

Choose a free point A on square using the point tool. We fix a original point from 4 vertex and name it as O. Measure the OA distance. Of cause, there is exist an one-to-one mapping that transform a point on square to a point on circle, so using this map, we can define a point B on circle that correlative with the point A on square.

Using this method, we define a point C on triangle that correlative with the point B on circle. After that, construct triangle ABC and create a free point on it. Chose this free point and the free point A on square, apply Construct | Locus. This loci will look like the square if the free point (named as "drag") is near point A, and so on.



Square to Circle to Triangle

We can change the triangle, circle and square and drag point "drag" to see how it works.

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