This is finding the perpendicular bisector of the line through p1 and p2 Given two points, there is a fold that places p1 onto p2 Given two points, p1 and p2, there is a unique fold that passes through both of them The following axioms are the operations which are allowed in origami folding. Origami can be used to show this ratio because certain origami folds yield answers which are similar to solving a cubic polynomial. You cannot construct the cube root of 2 because this number cannot be computed by a straightedge and compass' operations: addition, subtraction, multiplication, division, and taking square roots. How come the greeks did not solve it? At that time, the method to solve geometric problems was using an unmarked straightedge and a compass. This means to solve the problem, you need to find sides such that the ratio of the new side to the old side is the cube root of 3. Rearranging the terms yield x/y = 2^(1/3). Let x be the side of the new altar, and y be the side of the old altar. This problem is also known as the Delian problem. The correct solution is doubling the volume. Doubling of the sides of the altar caused the volume of the altar (which is cubic) to increase eight times (x^3 becomes (2x)^3 = 8x^3). What went wrong? The citizens did not follow instructions. The citizens doubled the sides of the altar, but the plague did not stop. The citizens went to the ocacle of Apollo at Delos which told them that the plague will stop when they've doubled the size of their altar. This project is to show how you can double the cube using origami (folding).Īccording to legend, there was a plague that was devastating Greece in 430BC. There are three classical geometric problems that the Greeks are unable to solve using an unmakred straightedge and compass: Doubling a cube Doubling the cube with origami
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