Desmos Dissections: Fellowship of Areas

We illustrate techniques of Geometric Dissection using a child’s jigsaw pieces (Chinese Tans). Follow Rabbit on his quest to learn the techniques that will uncover the 13 convex Tangrams!

Part 1: The Square that was Broken
# Triangulation # Internal Structure

Can you exploit Rabbit’s triangular grid to uncover the Square Tangram? Click here to try and here to view Rabbit’s solution!

Part 2: Surrounded
# Outlines # The Test

Can you exploit Squirrel’s outlines to uncover the Rectangle & Trapezium Tangrams? Click here to try.

Part 3: Sleights of Paw
# Twin Outlines # Slide Technique

How might Rabbit have turned Hedgehog’s Triangle into a Rectangle without turning any pieces over? Click here to view Hedgehog’s solution.

To see an animation of Rabbit’s solution, press play on T_2 in the sidebar of the following link. This is not the only solution. For an alternative application of Rabbit’s 2-square technique, click play on T_2 in the sidebar of the following link.

Part 4: In the Cross-Hares
# Perimeter Condition

To reposition and / or reorient Rabbit’s cross-hairs for yourself, click here.

Part 5: The Turnaround
# Superposition Technique

To take Hedgehog’s test for yourself, click here. See how similar the triangle of slide 10 is to the triangle of Part 4’s slide 8. In tandem with Owl’s perimeter condition then, Rabbit’s cross-hairs technique gave a good approximation of the final solution.

Part 6: Unhinged
# Hinged Dissections

To see a hinged form of Squirrel’s pieces animated, press play on T in the sidebar of the following link.

Part 7: Cornerstone
# Pythagoras

Want to see if you can arrange the pieces of the twin triangles into pieces of the twin squares? Click here to have a go for yourself!

Part 8: Under Lock and Key
# Mechanical Linkages # Scaffolds

Please click here to view animations of 4-bar linkages.

Want to devise your very own lock-and-key tiles? Click here and adjust the values of a, b, c, and d. Press play on T2 to animate your scaffold. You could leave a screen shot of your efforts (or a URL if you save your work) in the comments section!

Part 9: Lepus Ex Machina
# Final 5