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Paper-folding puzzles that explore geometry. Move the dot, change the thinking
Origami Dots is a collection of intriguing mathematical challenges that come from folding paper.
All the challenges are the same, fold the corner of the paper to a given dot and find the area that remains uncovered. Even with an unchanged question, a small move of the target dot can drastically change the logic needed to find the solution to the challenge. So the problems become increasingly complex, with possible solutions involving Pythagoras’ and similar triangles as well as trigonometry and algebra.
Insights learnt from earlier challenges can help with those that follow. However, if at point the challenge becomes too great, the answers can always be found by measurement with a ruler and directly calculating the area. The book encourages curiosity, a “find out what can you” discovery approach that creates interesting and varied journeys towards a solution. Starting with an approximate guess, these journeys are for all ages (10 years and over) to explore and discuss. To play concretely with paper while thinking and reasoning geometrically.
Thus, for teachers the book provides a rich source of challenges that have a similar appearance, yet hide an obvious method and require students to choose how to approach the problem. Comparing solution methods when checking the answers is also useful as the solutions highlight some fascinating facts linked with these simple folds.
The book divides into four explorations, each with a number of challenges.
- Exploration I - folding triangles,
- Exploration II - folding trapezia,
- Exploration III - problems in reverse and
- Exploration IV - two folds.
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