The use of trigonometry in ancient astronomical observations Introduction Trigonometry was improved initially as a tool for fixing problems in Greek Astronomy in the period of 300 BCE- 300 CE. The sine, cosine, tangent, cotangent terms were developed much later, however, the seeds were spangled by Greek astronomers and mathematicians. This presentation will cover the topic of the use of trigonometry in ancient astronomical observations. In this presentation, I will give basic understanding on trigonometry history. Furthermore, I will continue my presenting by giving some cases of trigonometry using in ancient astronomical observations. Body part Study of trigonometry was started at 2 millennium BC in Egyptian and Babylonian mathematics. Greek …show more content…
For finding ratio he derived set of inequalities as a bound of two quantities, because the trigonometry was not developed yet and he couldn’t use a calculator to find csc3o as the ratio. Finally, Aristarchus expressed that 1/20 < sin 3o <1/18, which means that the distance between the Earth and the Sun is 18 or 20 times greater than the distance between the Moon and the Earth. (Actually, distance between the Earth and the Sun is 400 times greater that the distance between the Moon and the Earth) (Rogers, 2010) Next huge step was made by Hipparchus, he used chord of a circle as a function of the corresponding arc. He made a table of chords of an arc, then many facts (including locations of 870 fixed stars) about specific stars were derived by him and which is written in his twelve-volume book. Therefore, the length of the lunar year and the month, the size of the Moon were written in his book. One of the mathematician who used trigonometry for astronomy was Eratosthenes. Eratosthenes worked as a librarian in Royal Library of Alexandria. Once, he noted that at every summer solstice at noon in the Siena, there were no shadow while reading a book. It meant that sunlight was beamed to the Alexandria horizontally and the sun appeared directly above the well. He knew that Alexandria and Siena was lying at the same meridian and that Alexandria is north of Syene for 500 …show more content…
Imaginary’ triangle was drawn and he estimated the angles between them. What he could find is that an angle of deviation between the sunlight and obelisk was approximately 7 degrees. Consequently, he noticed that difference between Aleksandria and Syene is 7 degree (approximately 1/50 of circumference). Therefore, every circle is divided into 360 degrees and the Earth is not an exception. Further, Eratosthenes multiplied the distance between two cities to 50 and got the circumference of the Earth of 25000 miles. Modern calculations estimate that the circumference of the Earth is 24894 miles and it can be seen that Eratosthenes was close to precise