Triangles and TrigonometryIntroduction
By the early 19th century, explorers had discovered most of the world. Trade and transportation was booming between distant countries, and this created a need for accurate maps of the entire planet.
Today we have satellites that can take photos from above – but 200 years ago, creating maps was a difficult and time consuming task. It was done by mathematicians like
Of particular interest was the quest to find the highest mountain on Earth. There were a few different candidates, but from hundreds of kilometers away, it was difficult to tell which one was the highest.
So how do you measure the height of a mountain?
Today we can use satellites to measure the height of mountains to within a few centimeters – but these did not exist when Radhanath was surveying India.
Climbers use altimeters to determine their altitude. These devices use the difference in air pressure at different heights. However this would have required someone to actually climb to the
You could also try using similar triangles, like we did in the previous course. This method requires knowing the
But there are more advanced geometric techniques, which
In this course you will learn about many different features and properties of triangles. These will allow you to measure the height of mountains, but they are also of fundamental importance in many other areas of mathematics, science and engineering.
Triangles are special because they are particularly strong. They are the only polygon that, when made out of wooden beams and hinges, will be completely rigid – unlike rectangles, for example, which you can easily push over.
COMING SOON – Animations
This property makes triangles particularly useful in construction, where they can carry heavy weights.
Triangles are also the simplest polygon, with the fewest sides. This makes them particularly well suited to approximating complex curved surfaces. This is done in physical building…
…but also in virtual worlds. In computer generated graphics (e.g. for movies or video games), all surfaces are approximated using a “mesh” of tiny triangles. Artists and software engineers need to know about geometry and trigonometry in order to be able to move and transform these triangles realistically, and to calculate their colour and texture.