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thinking-about-science.com | ||
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pfzhang.wordpress.com
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| | | | | Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. The second law provides a differential equation for the motion: given an initial position and an initial velocity, one can find the position at any given time $latex t\ge 0$. After Newton, one might wonder why the nature behaves... | |
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joe-antognini.github.io
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www.jeremykun.com
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| | | | | The standard inner product of two vectors has some nice geometric properties. Given two vectors $ x, y \in \mathbb{R}^n$, where by $ x_i$ I mean the $ i$-th coordinate of $ x$, the standard inner product (which I will interchangeably call the dot product) is defined by the formula $$\displaystyle \langle x, y \rangle = x_1 y_1 + \dots + x_n y_n$$ This formula, simple as it is, produces a lot of interesting geometry. | |
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jiggerwit.wordpress.com
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| | | In the texbook I'm using for a first course in algebraic geometry, the proof of Bezout's theorem is awful. Looking around, I find an abundance of awful proofs. A good proof is one that I would want to commit to memory. Here is a good proof of Bezout's theorem, which is due to Gurjar and... | ||
