Mathematicians estimated it by inscribing polygons in circles.

数学家通过在圆内接多边形来估算这个数值。

The circle, which is effectively a Reuleaux polygon with an infinite number of sides, has the largest.

圆是一个有洛正多边形有无数条边，有最大面积。

The tangram is a dissection puzzle consisting of seven flat polygons which are put together to form shapes.

七巧板是一个小块拼图游戏，由七个扁平多边形组成，这些多边形放在一起可以形成其他形状。

And over the years, more polygon lines were added, making the players look more and more lifelike.

并且经年累月，增加更多多边形线条，让球员们看起来越来越逼真。

Admittedly, this is a pretty ugly filled polygon.

诚然，这是一个非常丑陋填充多边形。

That’s because this algorithm doesn’t need to sort any polygons, which makes it faster.

这是因为该算法不需要对任何多边形进行排序，因此速度更快。

So no one was bisecting polygons to find Pi ever again.

所以再也有通过二分多边形来寻找圆周率。

Let's switch colors and switch polygons and put squares around these.

让我们切换颜色、切换多边形并在它们周围放置正方形。

This works with larger polygons too.

这也适用于更大多边形。

The rate at which a computer fills in polygons is called the fillrate.

计算机填充多边形速率称为填充率。

Importantly, it also works for some polygons with fewer sides, including heptagons, hexagons, and pentagons.

重要是， 它也适用于一些边数较少多边形，包括七边形、六边形和五边形。

If a pixel is entirely inside of a polygon, it gets fully colored.

如果一个像素完全在多边形内部，它就会完全着色。

They may be triangles or polygons, or different kinds of shapes that you don't normally expect in a building.

它们可能是三角形或多边形，或者您通常不会在建筑物中看到各种形状。

Consider this example scene with three overlapping polygons.

考虑这个具有三个重叠多边形示例场景。

But if the polygon only grazes a pixel, it’ll get a lighter shade.

但是如果多边形只擦过一个像素，它会得到一个更浅阴影。

Look at this beautiful teapot made out of polygons.

看看这个由多边形制成漂亮茶壶。

To make things easier to follow, we’re going to color the polygons differently.

为让事情更容易理解，我们要给多边形涂上不同颜色。

But for more complex shapes, triangles are better -- what are called polygons in 3D graphics.

但对于更复杂形状，三角形更好——在 3D 图形中称为多边形。

A collection of polygons like this is a mesh.

像这样多边形集合就是网格。

Although these models may have some smooth curves or squares and polygons, they're actually all  broken down into small triangles.

虽然这些模型可能有一些平滑曲线或正方形和多边形，但它们实际上都被分解成小三角形。