米和英尺哪个普遍（忘记米和英尺）

#大学英语听力#

Most of us learn some amount of Euclidean geometry in school.

我们大多数人在学校里学到了一些欧几里德几何。

We learn that the interior angles of triangles add up to 180°.

我们知道三角形的内角加起来是180°。

We learn how to prove that lines are parallel, or shapes are congruent or similar.

我们学习如何证明线是平行的，或者形状是一致的或相似的。

Even though we live on a planet that is not flat, our everyday intuition is on a scale that makes us feel like Euclidean geometry is the natural way to think about shapes, lengths, and angles.

即使我们生活在一个不平坦的星球上，我们的日常直觉的规模让我们觉得欧几里得几何是思考形状，长度和角度的自然方式。

I think it’s a real shame that more students are not exposed to non-Euclidean geometry early in their educations, but that’s a column for another time.

我认为，更多的学生在早期教育中没有接触到非欧几里德几何，这是一个真正的耻辱，但这是另一个时间的专栏。

Suffice it to say that if one is lucky enough to encounter geometry beyond that which takes place on a perfectly flat plane, one will learn that there is much more to geometry than two-column proofs and the Pythagorean theorem.

可以这样说，如果一个人足够幸运地遇到在完美平面上发生的几何学以外的几何，人们就会了解到几何学不仅仅是两列证明和毕达哥拉斯定理。

The intuition we develop in Euclidean geometry does not prepare us well for non-Euclidean geometry.

我们在欧几里德几何学中发展的直觉并没有为我们为非欧几里德几何学做好准备。

One of the delights I found when I first started studying hyperbolic geometry (one of the flavors of non-Euclidean geometry) was that many things that seem so obvious as not to require any kind of justification are flat-out wrong when we leave the flat Euclidean plane.

当我第一次开始研究双曲几何(非欧几里德几何的一种风格)时，我发现的乐趣之一是，当我们离开平坦的欧几里德平面时，许多看起来如此明显而不需要任何理由的事情都是彻头彻尾的错误。

For example, in non-Euclidean geometry, there is no such thing as a pair of triangles that are similar but not congruent.

例如，在非欧几里得几何中，没有一对相似但不全等的三角形。

The geometry of a sphere is another flavor of non-Euclidean geometry, so we can think about it on a globe.

球体的几何是非欧几里得几何的另一种风格，所以我们可以在球体上思考它。

On the Earth, there is a triangle that connects the North Pole with Quito (the capital of Ecuador) and Libreville (the capital of Gabon).

在地球上，有一个三角形连接北极与基多(厄瓜多尔的首都)和利伯维尔(加蓬的首都)。

This triangle is close to being a triangle with three right angles, or 270° of internal angle.

此三角形接近于具有三个直角或270°内角的三角形。