How to make an equilateral triangle

How to make an equilateral triangle - Easy tutorial

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@einsteingonzalez4336 4 жыл бұрын

So I've experienced this before. It's called "Neusis". It's a technique that requires sliding a ruler while measuring a certain distance between two lines, and they're like catchlines fishing for those specific two points on a ruler that make up that certain distance on that same ruler. An interesting property that neusis has it that it can trisect an angle (that is, divide an angle into 3 EQUAL parts) and construct other polygons not constructible with compass and straightedge. The heptagon is a great example as it's the simplest polygon that minimally requires neusis and NOT compass and straightedge. Based on those, we can solve cubic, quartic, and some solvable quintic equations. Cubic equations are equations with degree 3 (degree means the highest exponent in a polynomial), i.e. 𝓍³+𝓍²-2𝓍-1. You might visualize something like (𝒂+𝒃)³=𝒂³+3𝒂²𝒃+3𝒂𝒃²+𝒃³ as a cube with side length 𝒂+𝒃. Quartic equations are equations with degree 4, and can be visualized with a 4D (that is, 4-dimensional) version of a cube, called a tesseract, with side length 𝒂+𝒃. Quintic equations are equaitons with degree 5, and can be visualized with 5D (that is, 5-dimensional) version of a cube, called a penteract, with side length 𝒂+𝒃. Notice that I said "some solvable quintics"? That's because thanks to the Abel-Ruffini theorem, it's impossible to have the general quintic equation to be expressed EXACTLY in roots/radicals, and the same goes for polynomials with degree 6 and greater. The converse is true for degrees 0 to 4, but formulas for solving cubic and quartic polynomials (degrees 3 and 4 respectively) aren't taught in schools because they're both more complicated than the quadratic formula. Hope you've learned something about this method!