It's almost impossible to think of something that's made without the help of mathematics, buildings, transport, technology, medicine, even clothes and food, or rely on numbers, measurements and sums.

想不借助數學、建築、交通、科技、醫藥，甚至衣食住行，或者依靠數字、測量、求和，幾乎是不可能的。

Early pioneers discovered and explored the world using great ingenuity and varied mathematical skills, navigating by the sun and stars to find their way by measuring their position on relation to key points on Earth, they could navigate on travel thousands of kilometers.

早期的拓荒者用偉大的智慧和多樣的數學技巧發現和探索世界，通過測量他們與地球上的關鍵點的位置，通過太陽和星星找到他們的方向，他們可以在旅行數千公里的地方航行。

The surface of the earth can be divided like a chessboard with the lines of latitude on longitude.

地球表面可以像棋盤一樣劃分，經線上有緯線。

Using maths Onda tool called a sexton navigators could find their latitude and longitude by measuring the angle between two objects relative to the horizon.

使用被稱為六分儀的數學Onda工具，航海家可以通過測量兩個物體相對於地平線的角度來找到他們的經緯度。

It was very complicated involving calculations, celestial maps on charts.

這是非常複雜的，涉及到計算，天體圖在圖表上。

The principle was that an object would be positioned above a certain point of latitude and longitude at a particular time of day.

其原理是，在一天中的某一特定時間，物體會被定位在某一經緯度點之上。

This made positioning possible.

這使得定位成為可能。

Now, every point on each line has its own number, known as a coordinate.

現在，每條線上的每個點都有自己的編號，稱為座標。

So it's possible to find anywhere on the globe with just two numbers where the lines cross modern computers using similar maths, confined any location using the global positioning system, or GPS.

所以，只要用兩個數字就可以在全球任何地方找到線條交叉的地方，現代計算機使用類似的數學，用全球定位系統或GPS限制任何位置。

This network of 24 satellites 18,000 kilometers above the Earth is capable of locating any position to within 3.5 m and tracking journeys to any destination.

這個由24顆衛星組成的網絡在地球上空18,000公里處，能夠將任何位置定位在3.5米以內，並追蹤到任何目的地的行程。

GPS was originally developed for the U.

GPS最初是為美國開發的。

S military but is today available in numerous vehicles on Elektronik devices.

S軍事，但今天在眾多車輛上Elektronik設備。

So how does GPS calculate your position with the same mathematical measurements that our ancestors used?

那麼，GPS是如何用我們祖先使用的數學測量方法來計算你的位置的呢？

Let's say you want to find your current position using GPS at all times.

比方說，你想隨時用GPS找到你當前的位置。

You are in the line of sight of a least four satellites.

你在至少四顆衛星的視線範圍內。

A minimum of three.

至少三個。

Locate your position using latitude and longitude.

用經緯度定位你的位置。

By measuring the distance and angle between three satellites and your smartphone.

通過測量三顆衛星和你的智能手機之間的距離和角度。

They can pinpoint you exactly.

他們可以準確的定位你。

The fourth calculates your altitude.

第四種計算你的高度。

This network of orbiting satellites constantly transmit signals at the speed of light, so all this happens in the blink of an eye complex.

這個由軌道衛星組成的網絡不斷地以光速傳輸信號，所以這一切都發生在眨眼間的複雜。

Maths then visualizes your position in a three D landscape.

數學則將你的位置直觀地展現在三D景觀中。

Even if you are at the top of a mountain, GPS technology can now be found everywhere.

即使你在山頂，現在GPS技術也可以隨處可見。

The same technology also makes it possible to remotely pilot small vehicles and has turned the driverless car into a reality maths made it possible for our ancestors to discover the world on today.

同樣的技術也使得遠程駕駛小型車輛成為可能，並將無人駕駛汽車變成了現實數學讓我們的祖先發現今天的世界成為可能。

Maths makes it easier than ever for us to travel the globe using whatever form of transport we wish.

數學讓我們比以往任何時候都更容易使用任何形式的交通工具進行環球旅行。