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The Beginnings of Trigonometry
Transcript of The Beginnings of Trigonometry
2000 BCE EGYPTIANS AND BABYLONIANS ACHIEVEMENTS
- The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".
The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere. The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.
1000 BCE Greek and Hellenistic Advancements
- Ancient Greek and Hellenistic mathematicians made use of the chord of a circle when further developing the pre-beginnings of trigonometry. Due to this relationship between a chord and the other parts of a circle, a number of trigonometric identities and theorems that we study today were also known to Hellenistic mathematicians, but in their equivalent chord form.
- Although there is no actual trigonometry in the works of Euclid and Archimedes, in the strict sense of the word, there are theorems presented in a geometric way (rather than a trigonometric way) that are equivalent to specific trigonometric laws or formulas. For instance, propositions twelve and thirteen of book two of the Elements are the laws of cosine for obtuse and acute angles, respectively.
160 BCE HIPPARCHUS " FATHER OF TRIGONOMETRY" IS BORN
- Hipparchus, a Greek astronomer and mathematician, is often fondly referred to as "the father of trigonometry." Using a very primative form of trigonometry using circles and chords, Hiparchus compiled the first know star catalog and developed a system of identifying places on the surface of the earth by their latitude and longitude. This system is still in use to some extent today.
120 PTOLMEY PRESERVES AND SPREAD TRIGONOMETRY IDENTITIES
- Some 300 years after Hipparchus developed the basic of trig, Ptolemy expaned on his works greatly. Since most of Hipparchus' works had been lost, it was largely due to Ptolemy that the fundamental ideas of trigonometry were presented to the world. Ptolemy is also famous for incorrectly supporting the idea that our universe was earth-centered and that Asia extended much further west than it actually did
940 ARAB SCHOLAR DEVELOP TANGENT RATIO
- Albuzjani, an Arab scholar, is born. Albuzjani furthered the field of trig by introducing a new trig function when he constructed his table of tangent ratios.
1175 TRANSLATION OF PTOLMEY'S FURTHERS DEVELOPMENT
- Gerardo of Cremona works to translate the works of Ptolemy and Hipparchus from Arab into Latin
1945 TRIGONOMETRY IS REVIVED AND ADVANCED IN EUROPE
- Johann Regiomontanus helps to fix many of the translation errors in Gerardo's work and creates his own modern exposition and study on trigonometry
1595 TRIGONOMETRY GETS ITS NAME!
- The field begins to take on a language of its own (turning from Latin to Greek) and in 1595 the first known instance of the work "trigonometry," (from the Greek: trigonon=triangle, metron=to measure). This replaced a previous Greek term "goniometry" that was previously used to describe teh study of angle measurement.
1600 SINE, COSINE AND TANGENT ARE BORN
Albert Girard becomes the first mathematician to use the sine, cosine, and tangent abbreviations that are now so common (sin, cos, tan). Students still use these abreviations in math classrooms around the country
1667TRIGONOMETRY EXPAND BEYOND ITS ORIGINAL USES
- Trig begins to be used for more than just an tool of astronomy measurements. In 1667, Abraham DeMoivre created a trigonometry of imaginary numbers. This allows the mathematical field to extend in directions with many far-reaching consequences. These inventions and developments made it possible for such modern day sciences as aerospace engineering and computer-generated landscapes to be developed.
1800 GIVE ME A WAVE (SIN, COS, TAN THATS IS)
- Trigonometry once again causes a stir, when Joseph Fourier publishes his studies taht show how equations built from repeated sine and cosine waves can be used to construct a better understanding of the mechanics of light, heat, and sound. Our modern day Physics classrooms would not be the same without this discovery.
1849 TRIGONOMETRY MEASURES EVEREST
In November 1849, a team of scientists from the English develop the Great Trigonometrical Survey of India (which took five expeditions and more than 100 years to complete). As part of this survey, teams were set out to use trig and indirect measurement to calculate the peak of Mt. Everest. The measurement turned out to be 29,002 feet. The peak was named Everest because of one of the members of the surveying team on this expedition. Today, satellites obriting in space have placed Everest's height at 29,028. This signifies the awesome power of trig even with all of the modern convienences of today's mathematical studiesI.
500 BCE EUCLID AND ARCHIMEDES CONTIBUTE
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