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analytic_geometry.md

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 # Analytic Geometry
 
-Analytic geometry is part of [mathematics](math.md) that solves [geometric](geometry.md) problems with [algebra](algebra.md); for example instead of finding an intersection of a [line](line.md) and a [circle](circle.md) with ruler and compass, analytic geometry finds the intersection by solving an equation. In other words, instead of using pen and paper we use numbers. This is very important in computing as computers of course just work with numbers and aren't normally capable of drawing literal pictures and drawing results from them -- that would be laughable (or awesome?). Analytic geometry finds use especially in such fields as [physics simulations](physics_engine.md) ([collision](collision.md) detections) and [computer graphics](graphics.md), in methods such as [raytracing](raytracing.md) where we need to compute intersections of rays with various mathematically defined shapes in order to render 3D images. Of course the methods are used in other fields, for example [rocket science](rocket_science.md) and many other physics areas. Analytic geometry reflects the fact that geometric and algebraic problem are often analogous, i.e. it is also the case that many times problems we encounter in arithmetic can be seen as geometric problems and vice versa (i.e. solving an equation is the same as e.g. finding an intersection of some N-dimensional shapes).
+Analytic geometry is part of [mathematics](math.md) that solves [geometric](geometry.md) problems with [algebra](algebra.md); for example instead of finding an intersection of a [line](line.md) and a [circle](circle.md) with ruler and compass, analytic geometry finds the intersection by solving an [equation](equation.md). In other words, instead of using pen and paper we use numbers. This is very important in computing as computers of course just work with numbers and aren't normally capable of drawing literal pictures and drawing results from them -- that would be laughable (or awesome?). Analytic geometry finds use especially in such fields as [physics simulations](physics_engine.md) ([collision](collision.md) detections) and [computer graphics](graphics.md), in methods such as [raytracing](raytracing.md) where we need to compute intersections of rays with various mathematically defined shapes in order to render 3D images. Of course the methods are used in other fields, for example [rocket science](rocket_science.md) and many other physics areas. Analytic geometry reflects the fact that geometric and algebraic problem are often analogous, i.e. it is also the case that many times problems we encounter in arithmetic can be seen as geometric problems and vice versa (i.e. solving an equation is the same as e.g. finding an intersection of some N-dimensional shapes).
 
 [Fun](fun.md) fact: approaches in the opposite direction also exist, i.e. solving mathematical problems physically rather than by computation. For example [back in the day](back_then.md) when there weren't any computers to compute very difficult [integrals](integral.md) and computing them by hand would be immensely hard, people literally cut physical function plots out of paper and weighted them in order to find the integral. Awesome oldschool [hacking](hacking.md).