Posts
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创意诗
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How To Reject a Confession of Love Euphemistically
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How to Solve Gamma Function
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100 Things You Can Do To Improve Your English
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Canvas Clock
螃蟹在剥我的壳，笔记本在写我。
漫天的我落在枫叶上雪花上。
而你在想我。
Version 1 Thank you so much for your interest in my boyfriend intern 2018 position. Unfortunately, I have decided not to move forward with you as a candidate at this time. I received an unprecedented amount of confessions, and we decide to continue the process with other candidates with a stronger match. This is never an easy decision. I really do appreciate your interest and hope that you’ll keep me in mind for the future. I will keep your love letter in file, and, however, look forward to reaching out to you with right positions. In the meantime, we wish...
I. Theoretical Analysis Gamma Function is defined in the following, \[\Gamma(n) = \int_{0}^{\infty} \mathrm{e}^{-x}x^{n-1}\mathrm{d}x.\] Using integration by parts, one sees that: \[\Gamma(n) = -[\mathrm{e}^{-x}x^{n-1}]_0^{\infty} + (n-1)\int_{0}^{\infty} \mathrm{e}^{-x}x^{n-2}\mathrm{d}x = (n-1)\Gamma(n-1).\] From the above calculation，and note that \[\Gamma(1) = \int_{0}^{\infty} \mathrm{e}^{-x}\mathrm{d}x = 1\\ \Gamma(1/2) = \int_{0}^{\infty} \mathrm{e}^{-x}x^{-1/2}\mathrm{d}x = 2\int_{0}^{\infty} \mathrm{e}^{-y^2}\mathrm{d}y = \sqrt{\pi},\] where \(y^2 = x\). If \(n\) is a positive integer, one can obtain: \[\Gamma(n) = (n-1)(n-2)\cdots 1 \cdot \Gamma(1) = (n-1)!,\] \[\Gamma(n+\frac{1}{2}) = (n-\frac{1}{2})(n-\frac{3}{2})\cdots\frac{1}{2}\Gamma(\frac{1}{2})= (n-\frac{1}{2})(n-\frac{3}{2})\cdots\frac{1}{2}\sqrt{\pi}.\] Appendix: Integral calculus（\(y\equiv \sqrt{a}[x+(b/2a)]\)） \[\int_{-\infty}^{+\infty}\mathrm{e}^{-(ax^2+bx)}\mathrm{d}x = \int_{-\infty}^{+\infty}\mathrm{e}^{-y^2 + (b^2/4a)}\frac{1}{\sqrt{a}}\mathrm{d}y = \frac{1}{\sqrt{a}}\mathrm{e}^{b^2/4a}\int_{-\infty}^{+\infty}\mathrm{e}^{-y^2}\mathrm{d}y = \boxed{\sqrt{\frac{\pi}{a}}\mathrm{e}^{b^2/4a}}.\] If it meets a condition \(e^{-x^2} > 0\), obviously given that, \[I...
Don’t be afraid to make mistakes. Be confident. People can only correct your mistakes when they hear you make them. Surround yourself in English. Put yourself in an all English speaking environment where you can learn passively. The best way to learn is through speaking. Practise every day. Make yourself a study plan. Decide how much time a week you are going to spend studying and stick to it. Establish a routine. Tell your family and friends about your study plan. Get them to push you to study and also don’t let them interrupt you. Practise the 4 core skills:...
Build an analog clock using HTML canvas. Table of contents 1 Clock Intro 1.1 Create the Canvas 1.2 Code Explained 2 Clock Face 2.1 Draw a Clock Face 2.2 Code Explained 3 clock Numbers 3.1 Draw Clock Numbers 3.2 Example Explained 4 Clock Hands 4.1 Draw Clock Hands 4.2 Example Explained 5 Clock Start 5.1 Start the Clock 5.2 Example Explained 1 Clock Intro 1.1 Create the Canvas The clock needs an HTML container. Create an HTML canvas: HTML code: <!DOCTYPE html> <html> <style> canvas { -webkit-border-radius: 60px; border-radius: 60px; background-color: #FF91AF } </style> <body> <canvas id="canvas" width="400" height="400"></canvas> <script>...