Keep Thriving https://wiki.joak.org/ 2026-04-19T06:49:39+00:00 https://wiki.joak.org/ https://wiki.joak.org/_media/favicon.ico text/html 2025-12-30T09:17:43+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/public:math:tessellation?rev=1767086263&do=diff Tessellation 平面密铺 * 知乎上非常好的一篇文,by 陆zz 五边 不产生周期性图形的密铺 * 帽子、乌龟和幽灵：<https://www.nhatcher.com/post/on-hats-and-sats/> * 以下来自：<https://github.com/ruanyf/weekly/blob/master/docs/issue-379.md> * 2022年，一个业余数学家 David Smith 发现了一个有点像帽子的奇特形状： 这个形状的奇特之处在于，它可以无限不重复地铺满整个空间，且不形成周期性的重复图案。… text/html 2025-12-30T09:17:13+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/?image=public%3Amath%3Apaper.png&ns=public%3Amath&rev=1767086233&tab_details=history&media_do=diff&do=media <img src="https://wiki.joak.org/_media/public:math:paper.png?w=500&amp;h=500&amp;tok=05fdc8" alt="paper.png" loading="lazy" width="500" height="500" /> text/html 2025-12-30T09:10:01+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/?image=public%3Amath%3Aturtle.png&ns=public%3Amath&rev=1767085801&tab_details=history&media_do=diff&do=media <img src="https://wiki.joak.org/_media/public:math:turtle.png?w=500&amp;h=500&amp;tok=536fc2" alt="turtle.png" loading="lazy" width="500" height="500" /> text/html 2025-12-30T09:10:00+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/?image=public%3Amath%3Aspectre.png&ns=public%3Amath&rev=1767085800&tab_details=history&media_do=diff&do=media <img src="https://wiki.joak.org/_media/public:math:spectre.png?w=500&amp;h=500&amp;tok=22771e" alt="spectre.png" loading="lazy" width="500" height="500" /> text/html 2025-12-30T09:09:24+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/?image=public%3Amath%3Asimple-tilling.png&ns=public%3Amath&rev=1767085764&tab_details=history&media_do=diff&do=media <img src="https://wiki.joak.org/_media/public:math:simple-tilling.png?w=500&amp;h=500&amp;tok=862a64" alt="simple-tilling.png" loading="lazy" width="500" height="500" /> text/html 2025-12-30T09:08:31+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/?image=public%3Amath%3Ahat-marked.png&ns=public%3Amath&rev=1767085711&tab_details=history&media_do=diff&do=media <img src="https://wiki.joak.org/_media/public:math:hat-marked.png?w=500&amp;h=500&amp;tok=ccac95" alt="hat-marked.png" loading="lazy" width="500" height="500" /> text/html 2025-08-12T08:34:51+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/public:math:start?rev=1754987691&do=diff Mathematics Useful * 美国数学学会认可的教科书 * ProofWiki 定理证明收集wiki 问题 * Funny Formula * 赠券收集问题 * 欧拉公式 Euler's formula * Tessellation 平面密铺 子分类 * 数论 Number Theory * 图论 Graph Theory * 统计学 Statistics * 数学分析 Mathematical Analysis Tools * LaTeX Fun * Conway's Game of Life * <http://mingplusplus.com/game-of-life/> * 本福特定律（Benford's law）：<https://zh.wikipedia.org/wiki/%E6%9C%AC%E7%A6%8F%E7%89%B9%E5%AE%9A%E5%BE%8B> * 描述了真实数字数据集中首位数字的频率分布。一堆从实际生活得出的数据中，以1为首位数字的数的出现概率约为总数的… text/html 2025-07-18T08:28:09+00:00 oakfire (oakfire@undisclosed.example.com) https://wiki.joak.org/public:math:funny_formula?rev=1752827289&do=diff Funny Formula * \[ 3^3+4^3+5^3=6^3 \] * 莱布尼茨圆周率公式 \[ \frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \cdots \] * 巴塞尔问题解 \[ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \] * 高斯积分 \[ \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} \] * 斯特林公式 Stirling Approximation: \[ n! \approx \sqrt{2\pi n}\, \left(\frac{n}{e}\right)^{n} \]