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# Analytic Geometry
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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 and a circle with ruler and compass, analytic geometry finds the intersection by solving an equation. 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. Analytic geometry finds use especially e.g. in [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).
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[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).
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# Dog
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Here is our dog. He doesn't judge you, he loves unconditionally. No matter who you are or what you did, this doggo will always be your best friend <3 We should all learn from this little buddy.
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Send this to anyone who's feeling down :)
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```
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__
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_ / \
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(( / 0 0)
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\\___\/ _o)
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( | WOOOOOOOF
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| /___| |(
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|_)_) |_)_)
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```
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# Programming Tips
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This is a place for sharing some practical programming tips.
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- **add by small steps**: When adding features/functionality etc. into your code, do it by very small steps and test after each step. Do NOT add multiple things at once. If you add 3 features at once and then find out the program doesn't work, you will have an extremely hard time finding out the bug because it may be in feature 1, feature 2, feature 3 or ANY COMBINATION of them, so you may very well never find the bug. If you instead test after adding each step, you find potential bugs immediately which will make fixing them very quick and easy.
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- **no indentation for temporary code**: Tiny "workflow" tip: when adding new code, keep it unindented so that you know it's the newly added code and can delete it at any time. Only when you test the added code, indent it correctly to incorporate it as the final code. Of course, this fails in languages where indentation matters ([Python](python.md) cough cough) but similar effects can be achieved e.g. by adding many empty lines in front of/after the temporary code.
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- **comments/preprocessor to quickly hide code**: It is a basic trick to comment out lines of code we want to temporarily disable. However preprocessor may work even better, e.g. in C if you want to be switching between two parts of code, instead of constantly commenting one part and uncommenting the other just use `#if 0` and `#else` directives around the two parts. You can switch between them by just changing 0 to 1 and back.
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