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www.themathdoctors.org | ||
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jaydaigle.net
We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating. |
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liorsinai.github.io
[AI summary] This blog post explains the different methods for representing and performing rotations in 2D space, including polar coordinates, Cartesian matrices, and complex numbers, while also introducing the concept of quaternions for future 3D rotations. |
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www.kuniga.me
NP-Incompleteness: |
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thenumb.at
Or, where does that \(\sin\theta\) come from? Integrating functions over spheres is a ubiquitous task in graphicsand a common source of confusion for beginners. In particular, understanding why integration in spherical coordinates requires multiplying by \(\sin\theta\) takes some thought. The Confusion So, we want to integrate a function \(f\) over the unit sphere. For simplicity, lets assume \(f = 1\). Integrating \(1\) over any surface computes the area of that surface: for a unit sphere, we should end... |
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