[{"content":"KaTeX Inline and Basic When \\(a \\ne 0\\), there are two solutions to \\(ax^2 + bx + c = 0\\) and they are\n$$ x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a} $$\nThe Lorenz Equations $$ \\begin{aligned} \\dot{x} \u0026amp; = \\sigma(y-x) \\\\ \\dot{y} \u0026amp; = \\rho x - y - xz \\\\ \\dot{z} \u0026amp; = -\\beta z + xy \\end{aligned} $$\nThe Cauchy-Schwarz Inequality $$ \\left( \\sum_{k=1}^n a_k b_k \\right)^2 \\leq \\left( \\sum_{k=1}^n a_k^2 \\right) \\left( \\sum_{k=1}^n b_k^2 \\right) $$\nA Cross Product Formula $$ \\mathbf{V}_1 \\times \\mathbf{V}_2 = \\left| \\begin{matrix} \\mathbf{i} \u0026amp; \\mathbf{j} \u0026amp; \\mathbf{k} \\\\[0.3em] \\frac{\\partial X}{\\partial u} \u0026amp; \\frac{\\partial Y}{\\partial u} \u0026amp; 0 \\\\[0.5em] \\frac{\\partial X}{\\partial v} \u0026amp; \\frac{\\partial Y}{\\partial v} \u0026amp; 0 \\end{matrix} \\right| $$\nThe probability of getting k heads when flipping n coins is $$ P(E) = {n \\choose k} p^k (1-p)^{ n-k} $$\nAn Identity of Ramanujan $$ \\frac{1}{\\Bigl(\\sqrt{\\phi \\sqrt{5}}-\\phi\\Bigr) e^{\\frac25 \\pi}} = 1+\\frac{e^{-2\\pi}} {1+\\frac{e^{-4\\pi}} {1+\\frac{e^{-6\\pi}} {1+\\frac{e^{-8\\pi}} {1+\\ldots} } } } $$\nA Rogers-Ramanujan Identity $$ 1 + \\frac{q^2}{(1-q)}+\\frac{q^6}{(1-q)(1-q^2)}+\\cdots = \\prod_{j=0}^{\\infty}\\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \\quad\\quad \\text{for $|q|\u0026lt;1$}. $$\nMaxwell\u0026rsquo;s Equations $$ \\begin{aligned} \\nabla \\times \\vec{\\mathbf{B}} -\\ \\frac1c\\ \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} \u0026amp; = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\[1.0em] \\nabla \\cdot \\vec{\\mathbf{E}} \u0026amp; = 4 \\pi \\rho \\\\[0.5em] \\nabla \\times \\vec{\\mathbf{E}}\\ +\\ \\frac1c\\ \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} \u0026amp; = \\vec{\\mathbf{0}} \\\\[1.0em] \\nabla \\cdot \\vec{\\mathbf{B}} \u0026amp; = 0 \\end{aligned} $$\nInline math: \\(\\varphi = \\dfrac{1+\\sqrt5}{2}= 1.6180339887…\\)\nBlock math: $$ \\varphi = 1+\\frac{1} {1+\\frac{1} {1+\\frac{1} {1+\\cdots} } } $$\n","date":"2022-08-12T09:00:00Z","permalink":"https://lr-ch.netlify.app/en/p/how-to-math/","title":"How to Math"},{"content":"Not a post Hello! World!\nTables Are Cool col 1 Hello $1600 col 2 Hello $12 col 3 Hello $1 ","date":"2022-08-11T01:00:00Z","permalink":"https://lr-ch.netlify.app/en/p/test-post/","title":"Test Post"}]