作者：nccb
原帖地址：http://sinepost.wordpress.com
1. Ready to Launch
This blog will primarily be about mathematics and computing: using computing to learn and apply mathematics. Both of these subjects suffer (to differing extents) from mis-perceptions, so let’s start by trying to clarify a few things.
這個博客主要是數學和計算：使用電腦來學習和應用數學。這些科目都遭受錯誤的看法（不同程度），讓我們開始試圖澄清一些事情。
Mathematics is often confused with arithmetic (which is onlya small part of mathematics). When thinking of maths, many people imagine numbers and figures: 6 + 7, the 9-times-table, and so on. The ability to do numeric calculations in your head is somewhat handy, but this is the 21st century: the calculator app on your phone can add and multiply numbers more reliably than you can. Arithmetic is dull and easily automated. Much more interesting, and more useful, are the steps before you get to the calculator. Understanding and using the concepts and rules is the interesting part of maths:knowingwhat to calculate is key, not the actual calculation. (NB: North American readers will have to live with my funny-looking abbreviation of math.)
數學經常和算術運算混淆（算數僅僅是數學的一小部分）。當提到數學時，許多人想象的是數字和數據：6+7，九九乘法表，等等。依靠人腦進行的數值計算能力雖然靈活方便，但這是21世紀：用手機上的計算器程序進行加減乘除比你自己運算更可靠。算術計算是枯燥和容易自動化的，而更有趣更實用的則是計算的步驟。理解和使用概念及規則是數學的有趣之處：關鍵是要知道怎樣計算，而不是實際的計算結果。
Meanwhile, computing is often confused with IT, system administration or computer repair. Understandably, people who have no experience of computing (because it almost died out in schools) confuse it with what they know to be useful computer skills: fixing the wireless connection, or operating a spreadsheet. But computing is not about using computers;computing is not about using Google, it’s aboutmaking Google: how do you create a searchable index of the web that can be queried by a huge network of machines in milliseconds, and how do you decide which page is likely to be the most relevant result? Those are the kinds of interesting problems that you can tackle in computing.
同時，計算機信息處理技術往往與IT，系統管理人員或電腦維修等概念相混淆。這也難怪，沒有計算機信息處理體驗（大部分學校不重視）的人認爲計算機信息處理就是所謂有用的計算機技能：修復無線連接，或操作電子表格等。但計算機信息處理技術不是關於如何使用計算機的;它也不是指如何使用谷歌瀏覽器，它卻涉及到如何設計谷歌瀏覽器：你如何來創建網站索引以便在毫秒級內滿足龐大的網絡搜索需求，以及如何決定哪些頁面是可能是最相關的結果？這些都是可以通過計算機信息處理來解決的各種有趣的問題。
The whole point of this blog is to find some useful areas of overlap between maths and computing, and try to explain some of the points where they cross: I anticipate covering geometry, mechanics (in the physics sense: motion and forces), and probably some probability and statistics too. This blog is for:
- Those who struggle to see the relevance and practical application of mathematics,
- Those who know some computing, but struggle with maths (you are not a small group!), and
- Those who want to accomplish mathematical tasks in their programs, especially geometry: moving at angle, collision detection and so on.
本博客的主旨是要找到一些關於數學和計算機信息處理技術之間的重疊領域，並試圖解釋它們之間的一些交叉點：預計將包括幾何學，力學（物理意義上的運動和力），以及一些概率和統計方面的內容。這個博客面向的是：
- 那些很難看到數學的現實意義和實際應用的人，
- 那些知道一些計算，但與與數學在鬥爭的人（這是一個很大的羣體），以及
- 那些想要在程序中完成數學工作，特別是幾何方面：特定角度的移動，碰撞檢測等的人。
I’ll primarily be usingGreenfoot for coding my examples, because developing Greenfoot is my day job — but the principles can always be applied in other 2D frameworks such as Scratch, etc.
因爲開發Greenfoot是我的日常工作，所以我將主要使用Greenfoot來編寫自己的例子，但是涉及的原理也能夠應用於其他2D程序框架下，比如Scratch等等。
PS：各示例源碼除了可在相關帖子給出的鏈接中下載，還可以在此統一下載：http://download.csdn.net/download/qianer/5709485