Pythagorean Theorem Proof

thingiverse

This is an example of a proof of the Pythagorean Theorem. The 3x3 and 4x4 boxes can be rearranged on this model to show that the areas will be the same as that of the 5x5 box. This allows for visual learners to fidgit with the Pythagorean Theorem and see how it truly works so that they not only have the formula memorized but also understand what that formula means. (B.B, C.F., and R.H., MAT 363 Fall '16) Citation: Our design project was inspired by mshscott's similar model. Print Settings Printer Brand: SeeMeCNC Printer: Rostock MAX Rafts: No Supports: No Notes: When printing this it seems to be more precise, at least in its appearance, the larger scaled that it is printed at. The current settings will print an accurate file but the spacing of the pieces when moved to form the 5x5 box will be more visually appealing as you increase the models size. Post-Printing Once all three of the files have been printed you must attach the 4x4 box to its proper pole on the base piece. The same thing must be done to the 3x3 hinged piece. One thing to keep in mind is that this model was created so that it would be hard to be dismantled once it was put together so double check that your pieces will be swiveling in the correct directions before pushing them all the way down onto your pegs as they will be very difficult to remove without breaking the pegs the are placed on. How I Designed This This model was created in 3 separate pieces: the 4x4 box, the 3x3 box, and the base piece. 4x4 Box: To create the 4x4 box we had to create a 4x4 cube. We then created a cylinder which we hollowed out and attached to the cube for the peg from the base piece to go through. 3X3 Box: This piece was modeled from the file supplied in the link above. We began by creating small cubes of the proper sizes, according to the example we used, and then we had to build the hinges in them. To build the hinges between the pieces we had to create small cylinders and make sure that the spacing was correct so that they didn't meld together. We then had to curve the edges so that the pieces would be able to rotate without running into one another. The Base: For this piece we created a 4x4, 3x3, and 5x5 cube with a very small height as the platforms. We then had to rearrange them so that the corners matched up. This took a significant amount of time as the angles were hard to get properly lined up. Once this was done we created a cube to fit in the middle and wirecut it into a triangle. We then raised that piece up so that it would be at the same height as our moveable pieces. We then created fairly flat triangular bases on the corners of the inner triangle in the same fashion to attach our pegs to. We placed cylinders on those bases and our whole base of the model was then complete. Custom Section We came upon some issues when creating this with the angles of the squares of the base, the sizing of the pegs/peg-holes, and when creating the hinge. We struggled particularly with the hinge because it continually melded together in the center and was thus unable to move.