藝術作品中的幾何學

Teach Perspective to Help with Geometry

My 60-second idea is that school 1）geometry should start with the science of 2）perspective. That would empower students to do some attractive， surprising， artistic things right away. They wouldn’t feel that they are passive 3）receptacles for useless information.

I’m naturally terrible at drawing， so it was a revelation to me how it’s possible， for example， to draw the way a 4）checker board actually looks from any angle by following some simple but very clever and logical steps. When I first learned that， which was quite recently， I did it dozens of times just because it’s fun. The first steps in perspective are easier and more engaging than 5）Euclidian geometry， and they can be 6）illustrated both with classic art works and with 7）striking modern photographs. I think one could package all this in a very 8）inviting way， and get geometry classes off to a beautiful start.

我的60秒奇思是教授幾何學應該從（教授）透視學開始。這能夠使學生立刻就去做一些吸引人的、令人驚奇的、有美感的事。他們不會覺得自己是在被動地接受無用的信息。

由于我天生就不擅長繪畫，所以畫畫對我來說是個揭露真相的過程。例如，（我）從任意一個角度去畫一個棋盤，通過采取一些簡單但卻非常巧妙而又富有邏輯的方法使它看起來跟實物一樣。當我第一次知道這些辦法，這也是最近的事了，僅僅是因為這很有趣，我就畫了幾十次。透視法的第一步比歐幾里得幾何學更簡單，也更吸引人。它們可以同時用經典的藝術作品和不同尋常的現代攝影作品來舉例說明。我覺得我們可以把所有這些包裝得很誘人，使幾何學課程有一個美麗的開端。