Playground

The Playground

Conic Generator This Java Sketchpad file is an animation that produces tangent envelopes of ellipses and hyperbolas.

Conic Generator II This Java Sketchpad file is an animation that produces ellipses and hyperbolas and their tangent envelopes.

Torus Games Download Tic-Tac-Toe, chess, and more ... played on a torus! Temporarily Unavailable.

Parabola Generator

Sketchpad Animations Inspired by Origami Quilts and Boxes More information is available under Resources. Only one of the original group of animations remains at this linked page.

Sketchpad Animations Inspired by Quilts

Affine Transformations Try the three buttons below.

Affine Transformation of a Triangle *

Click on the blue button to get an interactive sketch. The sketch shows a black triangle and its image under an affine transformation. The red points are all "live;" drag them to see how the red image changes as its black pre-image changes. The transformation is also "live." It is defined by the measures a,b,c,d,e, and f of the line segments shown, so just drag endpoints of the segments to change the transformation. The transformation is defined by (x',y')= (x,y)A + (e,f) and A is the matrix:

a c

b d

Click on the * to the left to play a matching game. Adjust the parameters (a,b,c,d,e,and f) so that the triangle's affine image (the red triangle) coincides with an equilateral triangle (the green triangle). Click here for an annotated script to produce an affine transformation.

Affine Transformation of a Circle This one is similar to the one above, except that it transforms a circle instead of a triangle.

Affine Transformation of a Parabola This one is similar to the one above, except that it transforms a parabola.

Desargues' Theorem Here's a start on projective geometry, with an illustration of Desargues' Theorem, created by Char Morrow. Is it 2-dimensinal or 3-dimensional?

Equilateral Triangle Dissection There is a way to cut up an equilateral triangle into pieces that can be reassembled to form a square. Click to see the method and a transformation of a tiling of the plane by equilateral triangles into a tiling by squares.

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Conic Generator		This Java Sketchpad file is an animation that produces tangent envelopes of ellipses and hyperbolas.
Conic Generator II		This Java Sketchpad file is an animation that produces ellipses and hyperbolas and their tangent envelopes.
Torus Games		Download Tic-Tac-Toe, chess, and more ... played on a torus! Temporarily Unavailable.
Parabola Generator
Sketchpad Animations Inspired by Origami Quilts and Boxes		More information is available under Resources. Only one of the original group of animations remains at this linked page.
Sketchpad Animations Inspired by Quilts
Affine Transformations		Try the three buttons below.
Affine Transformation of a Triangle	*	Click on the blue button to get an interactive sketch. The sketch shows a black triangle and its image under an affine transformation. The red points are all "live;" drag them to see how the red image changes as its black pre-image changes. The transformation is also "live." It is defined by the measures a,b,c,d,e, and f of the line segments shown, so just drag endpoints of the segments to change the transformation. The transformation is defined by (x',y')= (x,y)A + (e,f) and A is the matrix: a c b d Click on the * to the left to play a matching game. Adjust the parameters (a,b,c,d,e,and f) so that the triangle's affine image (the red triangle) coincides with an equilateral triangle (the green triangle). Click here for an annotated script to produce an affine transformation.
Affine Transformation of a Circle		This one is similar to the one above, except that it transforms a circle instead of a triangle.
Affine Transformation of a Parabola		This one is similar to the one above, except that it transforms a parabola.
Desargues' Theorem		Here's a start on projective geometry, with an illustration of Desargues' Theorem, created by Char Morrow. Is it 2-dimensinal or 3-dimensional?
Equilateral Triangle Dissection		There is a way to cut up an equilateral triangle into pieces that can be reassembled to form a square. Click to see the method and a transformation of a tiling of the plane by equilateral triangles into a tiling by squares.