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#= | |
Solves a geometry problem using linear algebra and Heron's formula | |
See: Red Flag Day Geometry | |
using Revise | |
Load with: includet("redflag.jl") | |
=# | |
using LinearAlgebra |
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/* | |
The PI License | |
Finds a four digit prime number n such that n is | |
- Balanced: A prime equidistant from the previous and subsequent prime numbers. | |
- Odious: A number is odious if the binary representation of the number as an odd number of 1's, and is evil if the number of 1's is even. | |
- Happy: Add the squares of the digits to get a new number. Continue the process and if you ever get to $1$, the original number is happy. | |
- Apocalyptic: If 2^n contains the sequence 666, then n is apocalyptic. | |
Author: John Peach |
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// Gmsh project created on Mon Jun 17, 2024 | |
SetFactory("OpenCASCADE"); | |
// Define points | |
L = 0.5; // Tube length | |
H = 0.05; // Tube width | |
N = 10; // Number of rectangles along length of the tube | |
Point(1) = {0, 0, 0, 1.0}; | |
Point(2) = {L, 0, 0, 1.0}; | |
Point(3) = {L, H, 0, 1.0}; |
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// Shape parameters | |
sphereRadius = 0.65; | |
cylinderRadius = 0.3; | |
cylinderHeight = 1.1; | |
// Top level difference operation | |
difference(){ | |
// Intersection of cube and sphere | |
intersection(){ |
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<!DOCTYPE html> | |
<html> | |
<head> | |
<meta name=viewport content="width=device-width,initial-scale=1"> | |
<meta charset="utf-8"/> | |
<script src="https://cdn.geogebra.org/apps/deployggb.js"></script> | |
</head> | |
<body> | |
<div id="ggbApplet"></div> |
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x | logx | Hr | Fit | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.000222026 | -3.653596397 | 0.356389604 | -0.125 | |||||||||||||
0.000279034 | -3.55434296 | 0.356389604 | -0.125 | |||||||||||||
0.00035068 | -3.455089522 | 0.37470064 | 0 | |||||||||||||
0.000440721 | -3.355836085 | 0.37470064 | 0 | |||||||||||||
0.000553882 | -3.256582648 | 0.502877892 | 0.125 | |||||||||||||
0.000696099 | -3.157329211 | 0.557811 | 0.125 | |||||||||||||
0.000874831 | -3.058075774 | 0.637158823 | 0.25 | |||||||||||||
0.001099456 | -2.958822336 | 0.692091931 | 0.375 | |||||||||||||
0.001381755 | -2.859568899 | 0.917928042 | 0.5 |
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