The Boot Kidz — Epicycles

Fun with Maths - Wellington Boot Epicycles

Karen Henry Educational Epicycles Fun Maths Science Wellington Boots Wolfram Alpha

Fun with Maths - Wellington Boot Epicycles

Here are 10 steps to create a Wellington Boot from rotating circles (epicycles). Ref 1: https://youtube.com/watch?v=qS4H6PEcCCA by Mathologer (recommend to subscribe) - Explanation of the maths Ref 2: https://mathematica.stackexchange.com/questions/171755/how-can-i-draw-a-homer-with-epicycloids by anderstood for the code Ref 3: Code file - if you need the code Ref 4: The welly image 1) Create an account (14-day free trial available) at https://mathematica.wolframcloud.com 2) Create a new Wolfram notebook (File -> New Notebook) Paste the following code into the top part of the notebook (takes a few seconds for Wolfram to recognise it): img = Import["https://cdn.shopify.com/s/files/1/0001/1319/files/wellington-boot-black-and-white.gif?9529291750893159073"];img = Binarize[img~ColorConvert~"Grayscale"];img = ImageResize[img,100];img = Blur[img,3];pts = DeleteDuplicates@   Cases[Normal@      ListContourPlot[Reverse@ImageData[img],        Contours -> {0.5}], _Line, -1][[1, 1]];center = Mean@MinMax[pts] & /@...

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