Trigonometry/Introduction
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[edit] Introduction to trigonometry
It is easy to explain in word-terms what trigonometry means, but it is more important to understand what mechanisms of thinking, which will help you understand not only trigonometry, but everything in life in a much more vivid way.
In mathematics, trigonometry is an important set of disciplines which relate to two and three dimensional objects; practically anything that you can see around you can be related to the principles of trigonometry and algebra -- in the real-world, it is very useful in engineering and construction, where its principles are important in accurately determining the lengths, sizes and areas of objects without having to actually create them first. Imagine the need to build a structure with only the basic land-area given to you: using the principles of trigonometry, you can easily calculate the geometric properties of objects to an unerring degree of accuracy.
Trigonometry, however, isn't just about using formulae to find the correct angle or size in school. It describes the relationships that occur naturally between objects and their similarity in structure. When we compare them using a similar set of ideas, it gives us a lot of power to understand the basis of other things in life beyond that of just their appearance. Even though we can look at a circle, an oval, square or rectangle, we can know that there are principles we can apply to their shape which can be expressed through one entity: the triangle.
[edit] A brief history of trigonometry
Originally, the Babylonians were the first to discover the measures of the angle, but it was not until the onset of the Greeks, who were the original pioneers in the field of trigonometry, and the inventors of a measure known as the "sexagesimal". In 2BC, a Greek man known as Hipparchus was thought to be the first person who devised a more complete idea of a trigonometric triangle. He produced a table of reference for solving a triangle's lengths and angles, by making a reference table of the lengths of the sides of the triangles for angles between 71o and 180o. This was what could be called the equivalent of a "sine table"; the basis of the modern sin function, which has become a crucial tool in the calculations for modern living, construction and manufacture. Sine tables were once used in some school systems in Europe and America, but have now been dropped for the use of the sin function on modern calculators, opting to focus more on the principles of trigonometry, rather than trigonometric values.
In his research, however, a crucial entity in recording was either lost, or not recorded simply because it may not have been thought of as important, or even thought of at all. This entity was known as the radius; half the length of the width of the circle, when measured from one side to another. Over 300 years later, Greeks adapted upon this measure by using the sexagesimal measure, and saying that the radius should be a fixed length of 60; r = 60.
An important figure, too, in geometry and trigonometry was Euclid. Euclid was a Greek mathematician, about whom almost nothing was known other than the works that he produced. Surprisingly, the work he is most renowned for, Elements, is an amazingly in-depth work for the time, as it covers in some detail the basic and more advanced aspects of geometry and trigonometry. Even though there is some uncertainty towards the originality of certain concepts contained within Elements, there is no doubt that Euclid is a very important figure in the discovery of trigonometric principles, because so much of what is known about geometric measure in trigonometry is comparable to his work.
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