A Greek Invention

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

During this time period many things were invented like the astrolabe, sextant, and caravel. The caravel was invented by the portuguese, was much less heavy so it could travel up rivers, was quicker for the longer journeys, and had a triangular sail instead of a rectangular sail. The astrolabe was an instrument that, in its earlier time, was used for astronomy and astrology but ended up mainly being used as a tool of navigation and to solve problems involving trigonometry, problems relating to time, and the position of the sun and stars. The astrolabe was invented by Hipparchus who lived from 190 BC - 120 BC and also made major contributions to trigonometry. Trigonometry is a type of math that involves the relations between a triangle’s angles and sides.

The mathematic that not only facilitated in the renaissance but provide the key a new science of nature from Galileo.

70,000+ years ago, Africans developed the systems of adding and subtracting as well as multiplication and division. Also, they were the first to make sense of fractions. Egyptians used geometric formulas to calculate the volume and area of items so that they could construct different structures. They also calculated distances and angles along with solving algebraic based on minimum resources, like the Nile River. The ancient Egyptians also theorized that a circle is equal to 360 degrees, and pi was estimated to be about 3.16. The same mathematics that we use today was discovered and advanced by ancient Africans, Egyptians to be

logarithms as it is for the forgotten trigonometric functions: it was easier and quicker for

Algebra is the key a successful life. If you know algebra it will help you to excel in the field that you want to specialize in.

Triangles in that were mostly use in this part of geometry are right triangles. There are two theorems that can be uses with the special right triangles, they are 45-45-90 triangle theorem and 30-60-90 triangle theorem. The legs of a 45-45-90 are the same. In a 30-60-90 triangle, the short leg is always opposite the 30 degrees angle, and basically everything lengths can be find after found out the short leg.

Nicolaus Copernicus was a polish astronomer and a cleric. At the age of ten his father died and his uncle took him in along with his brothers and sisters. His uncle wanted to make sure he had the best education possible. He went to three different Universities to learn math, science, law, medicine, and astronomy. A spot opened up in the church and his uncles connections got Copernicus the spot. He studied the Bible and became a priest like his uncle. With all of the income he was receiving it allowed him to not work and study the universe. He went on studying the solar system and it’s rotations. After spending twenty five years studying the earth and its rotation he came up with the theory that the sun is the center of the universe and

Since Geometry is interlinked with Astronomy and is useful for calculating spatial distances, both these subjects were learnt together in olden days. Not only that, Geometry has sprinkled its influence upon various other areas like art, land survey, civil engineering and architecture. You can find the overtones of Geometry in Science subjects like Physics also. Hence, Geometry has a vast role to play in the contour of Math learning and makes for successful understanding of related topics in Trigonometry and

“When I heard the learn’d astronomer, When the proofs, the figures, were ranged in columns before me, When I was shown the charts and diagrams, to add, divide, and measure them, When I sitting heard the astronomer where he lectured with much applause in the lecture-room.”

The more I study trigonometry, the more it seems like mathematical magic. The relationships between angles and sides that have been uncovered and rewritten as seemingly simple identities are definitely more than meets the eye. I am especially drawn to their all-inclusive nature. It does not matter what the side lengths or angle measurements of the triangle are; the laws of trigonometry are always applicable and accurate. Needless to say, I was quite intrigued when I came across something known as Morley’s Theorem which reads,

Nubian pyramids demonstrate the Nubians use of geometry as it would have been necessary to build such pyramids.

The Square Root of 2, after the Pythagorean theorem was established, the following question was put forth: If we had a square with each side a unit in length, and we also had a second square with double the area of the first square, how would the side of the second square compare to the side of the first square? This is the origin of the question regarding the square root of 2. The Pythagoreans could not solve the puzzle, and they finally faced up to the reality that no ratio of two whole numbers could express the value of the square root of 2, so they looked into

2) since you are in 10(C.B.S.E) your study of Trigonometry is concerned to 2-D only . even then you can try 3-d. Following is a description:

Finding the tangents to curve and area of a curve were the driving questions which motivated mathematicians in the 18th century to lay the foundations of calculus. Interestingly, the Greeks had already calculated the area of an ellipse by approximations. They constructed polygons, one inside and one around the ellipse which roughly were equivalent to the area of the ellipse.