我对高中学习几何学只有模糊的记忆。我喜欢它是因为您必须画画，而当我的一些同学讨厌做证明时，我没有’太在乎他们了。我把它们看作是一个难题，整个过程的逻辑吸引了我。我可以’t say I ever really 被爱 几何或发现它 好玩但是。
快进到上周末。我发现了“欧几里得”在Hacker News上。作为一种游戏，它提出了几何挑战。它’基本上与证明相同，但不是“证明这无聊的事情” it 挑战 您，并为您提供了一个带有几何图形的小工具栏“weapons”你可以申请。让我印象最深的一件事是，在您证明自己知道如何构造平行线或垂直线，或如何平移直线后，–with simpler tools–you gain new “shortcut buttons”工具栏中的这些任务。真好！
无论如何，所有这一切的重点是，学习会变得更加有趣’s 呈现为 有趣的挑战。我们中有多少人必须先记忆公理，然后定理，然后仔细研究无欢乐的证明，以学习几何？有了这个“Euclid the Game,”挑战因素使您前进，而您所拥有的东西’应该记住你只是“pick up”因为您需要它来解决挑战。最上面的樱桃是’解决挑战的方法不只是一种正确的方法，因为，几何形状很灵活。
> To appreciate the nature 和 significance of the coming “singularity,” it is important to ponder the nature of 指数增长. Toward this end, I am fond of telling the tale of the 在 ventor of 棋 和 his patron, the emperor of China. In response to the emperor’s offer of a reward for his new beloved game, the 在 ventor asked for a single grain of rice on the first square, two on the second square, four on the third, 和 so on. The Emperor quickly granted this seemingly benign 和 humble request. One version of the story has the emperor going bankrupt as the 63 doublings ultimately totaled 18 million trillion grains of rice. At ten grains of rice per square 在 ch, this requires rice fields covering twice the surface area of the Earth, oceans 在 cluded. Another version of the story has the 在 ventor losing his head.
> It should be pointed out that as the emperor 和 the 在 ventor went through the first half of the 棋 board, things were fairly uneventful. The 在 ventor was given spoonfuls of rice, then bowls of rice, then barrels. By the end of the first half of the 棋 board, the 在 ventor had accumulated one large field’s worth (4 billion grains), 和 the emperor did start to take notice. It was as they progressed through the second half of the 棋board that the situation quickly deteriorated. Incidentally, with regard to the doublings of computation, that’s about where we stand now–there have been slightly more than 32 doublings of performance since the first programmable computers were 在 vented during World War II.
> This is the nature of 指数增长. Although technology grows 在 the exponential domain, we humans live 在 a linear world. So technological trends are not noticed as small levels of technological power are doubled. Then seemingly out of nowhere, a technology explodes 在 to view. For example, when the Internet went from 20,000 to 80,000 nodes over a two year period during the 1980s, this progress remained hidden from the general public. A decade later, when it went from 20 million to 80 million nodes 在 the same amount of time, the impact was rather conspicuous.
> Joseph Needham posits that “image-chess,” a recreational game associated with divination, was developed 在 China 和 transmitted to India, where it evolved 在 to the form of modern military 棋. Needham notes that dice were transmitted to China from India, 和 were used 在 the game of “image-chess.”
> Another alternative theory contends that 棋 arose from 象棋 或其前身，自公元前2世纪起就存在于中国。李鸿章（David H. Li）是一位退休会计师，会计学教授和古代汉语译者，他假设汉新将军借鉴了刘博的早期游戏，以在公元前204-203年冬季开发出早期的中国象棋形式。但是，德国象棋历史学家彼得·巴纳沙克（Peter Banaschak）指出’s main hypothesis “毫无根据”. He notes that the “Xuanguai lu,”由唐朝大臣牛僧如（779–847）撰写，仍然是中国象棋变体的第一个真实来源 象棋.