In 2012, Mathematician Ian Stewart came out with an excellent and deeply researched book titled "In Pursuit of the Unknown: 17 Equations That Changed the World." 在 2012 年，数学家斯图尔特（Ian Stewart）出版了一本精彩而深入研究的著作，名为《追寻未知：改变世界的 17 个公式》。 His book takes a look at the most pivotal equations of all time, and puts them in a human, rather than technical context. 他的书着眼于有史以来最关键的方程式，并将它们置于普通人而非专业的背景中。 "Equations definitely can be dull, and they can seem complicated, but that's because they are often presented in a dull and complicated way," Stewart told Business Insider. "I have an advantage over school math teachers: I'm not trying to show you how to do the sums yourself." 「方程式肯定会显得沉闷，而且它们看起来很复杂，但那是因为它们经常以这样的方式呈现，」斯图尔特告诉 Business Insider。 「我比学校的数学老师更有优势：我不会试图告诉你如何自己算出它们。」 He explained that anyone can "appreciate the beauty and importance of equations without knowing how to solve them ... The intention is to locate them in their cultural and human context, and pull back the veil on their hidden effects on history." 他解释说，任何人都可以「欣赏方程式的美丽和重要性，而不去知道如何解它们…… 目的是将它们置于文化和人文环境中，并揭开它们对历史隐藏效应的面纱。」 Stewart continued that "equations are a vital part of our culture. The stories behind them — the people who discovered or invented them and the periods in which they lived — are fascinating." 斯图尔特继续说道，「方程式是我们文化的重要组成部分。他们背后的故事 —— 发现或发明它们的人以及他们生活的时期 —— 都很吸引人。」 Here are 17 equations that have changed the world: 以下是改变世界的 17 个方程式： Max Nisen contributed to an earlier version of this post. Max Nisen 为本文的早期版本做出了贡献。
The Pythagorean Theorem
Pythagoras, 530 BC What does it mean? The square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. 作用：直角三角形的斜边的平方等于其直角边的平方和。 History: Though attributed to Pythagoras, it is not certain that he was the first person to prove it. The first clear proof came from Euclid, and it is possible the concept was known 1,000 years before Pythagoras by the Babylonians. 历史：虽然认为毕达哥拉斯（Pythagoras）发现了这个公式，但不确定他是否是第一个证明它的人。第一个明确的证明来自欧几里得，而这个概念可能是在毕达哥拉斯之前 1000 年就被巴比伦人知道了。 Importance: The equation is at the core of much of geometry, links it with algebra, and is the foundation of trigonometry. Without it, accurate surveying, mapmaking, and navigation would be impossible. 重要性：勾股定理是几何的核心，它与代数联系起来，是三角学的基础。没有它，准确的测量、地图制作和导航将是不可能的。 In terms of pure math, the Pythagorean Theorem defines normal, Euclidean plane geometry. For example, a right triangle drawn on the surface of a sphere like the Earth doesn't necessarily satisfy the theorem. 在纯数学方面，毕达哥拉斯定理定义了正常的欧几里德平面几何。例如，在像地球一样的球体表面上绘制的直角三角形不一定满足该定理。 Modern use: Triangulation is used to this day to pinpoint relative location for GPS navigation. 现代用途：今天使用三角测量来确定 GPS 导航的相对位置。
Please add a nonce to your POST calls to prevent unauthorized access. Keep in mind, check_admin_referer alone is NOT bulletproof security. Do not rely on nonces for authorization purposes. Use current_user_can() in order to prevent users without the right permissions from accessing things.
Please sanitize, escape, and validate your POST calls
When you include POST/GET/REQUEST/FILE calls in your plugin, it's important to sanitize, validate, and escape them. The goal here is to prevent a user from accidentally sending trash data through the system, as well as protecting them from potential security issues. SANITIZE: Data that is input (either by a user or automatically) must be sanitized. This lessens the possibility of XSS vulnerabilities and MITM attacks where posted data is subverted. VALIDATE: All data should be validated as much as possible. Even when you sanitize, remember that you don't want someone putting in 'dog' when the only valid values are numbers. ESCAPE: Data that is output must be escaped properly, so it can't hijack admin screens. There are many esc_*() functions you can use to make sure you don't show people the wrong data. To help you with this, WordPress comes with a number of sanitization and escaping functions. You can read about those here: https://developer.wordpress.org/plugins/security/securing-input/ Remember: You must use the MOST appropriate functions for the context. If you're sanitizing email, use sanitize_email(), if you're outputting HTML, use esc_html(), and so on. Clean everything, check everything, escape everything, and never trust the users to always have input sane data.
