希腊字母表
一直想找个机会把希腊字母的读法都给记下来。
希腊字母源于腓尼基字母，腓尼基字母只有辅音，从右向左写，希腊语言元音发达，希腊人增添了元音字母。因为希腊人的书写工具是蜡板，有时前一行从右向左写完后顺势就从左向右写，变成所谓 “耕地”式书写，后来逐渐演变成全部从左向右写。字母的方向也颠倒了。罗马人引进希腊字母，略微修改将其变为拉丁字母，在世界广为流行。希腊字母广泛应用到学术领域，如数学等。西里尔字母也是由希腊字母演变而成。英语单词 alphabet（字母） ，源自通俗拉丁语 alphabetum，alphabetum 又源自希腊语 αλφαβητον (音译beton) ，即为前两个希腊字母 α（Alpha）及 β（Beta）所合成。
希腊字母对希腊文明乃至西方文化影响深远。《新约》里，神说：“我是阿尔法，我是欧米伽，我是首先的，我是最后的，我是初，我是终。”（圣经启示录22:13）。在希腊字母表里，第一个字母是 “Α，α ”（Alpha），代表开始，最后一个字母是 “Ω， ω” 欧米伽（Omega），代表终了。这正是《新约》用希腊语写作的痕迹。
下面是关于各个希腊字母的常用场景：
- $\alpha$ (lower case alpha) – a generic variable; an angle of a triangle
- $\beta$ (lower case beta) – a generic variable; a different angle of a triangle
- $\Gamma$ (capital gamma) – the gamma function; the graph of a function as a set of pairs; a graph in the sense of graph theory
- $\gamma$ (lower case gamma) – a closed curve (e.g., integrating over the real or complex plane)
- $\Delta$ (capital delta) – a change; the max degree of a graph
- $\delta$ (lower case delta) – a change; a small positive value that you may choose; an impulse
- $\epsilon$ (lower case epsilon) – a small arbitrary positive real number; an error rate
- $\zeta$ (lower case zeta) – the Riemann zeta function; a complex variable (like z)
- $\eta$ (lower case eta) – an error rate; a step size in an algorithm
- $\Theta$ (capital theta) – an angle; asymptotic equivalence
- $\theta$ (lower case theta) – an angle
- $\iota$ (lower case iota) – the inclusion function; an injective function or embedding
- $\kappa$ (lower case kappa) – curvature; connectivity; conditioning
- $\Lambda$ (capital lambda) – matrix of eigenvalues
- $\lambda$ (lower case lambda) – an eigenvalue of a matrix
- $\mu$ (lower case mu) – a measure; a mean;
- $\nu$ (lower case nu) – None. I hate this letter because I think it’s hard to draw and it’s too close to v.
- $\Xi$ (capital xi, like “ksee”) – None. It’s a weird letter that only a math troll would love. Too close to ≡ and conflicts with drawing bars on top of variables.
- $\xi$ (lower case xi) – a complex variable; I often draw it like a lightning bolt with a hat.
- $\Pi$ (capital pi) – a product;
- $\pi$ (lower case pi) – the constant~3.14; a projection
- $\rho$ (lower case rho) – projection; a rate; a rotation; a correlation
- $\Sigma$ (upper case sigma) – sum; an alphabet of symbols; covariance matrix
- $\sigma$ (lower case sigma) – standard deviation; a symmetry; a reflection; a sign +/-1.
- $\tau$ (lower case tau) – a symmetry; a translation; if I really want to use \pi but it would be confusing, so I draw it standing like a bird holding up one of its legs.
- $\Upsilon$ (capital upsilon) – ??
- $\upsilon$ (lower case upsilon) – Too close to “u,v” not used.
- $\Phi$ (capital phi, like “fai”, though many pronounce “fee”) – a general function; a potential function
- $\phi$ or $\varphi$ (lower case phi) – a function/morphism; golden ratio; totient function
- $\chi$ (lower case chi, like “kai”) – a character; a statistic; the indicator function of an event; Euler characteristic
- $\Psi$ (capital psi, like “sai”) – a function/morphism;
- $\psi$ (lower case psi) – a function/morphism
- $\Omega$ (capital omega) – a lower bound
- $\omega$ (lower case omega) – a lower bound; a complex cube root of 1
