Early Trigonometry
Early trigonometry
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".[6]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.[2] Based on one interpretation of the Plimpton 322 cuneiform tablet (c. 1900 BC), some have even asserted that the ancient Babylonians had a table of secants.[7] There is, however, much debate as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table.The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.[2] The Rhind Mathematical Papyrus, written by the Egyptian scribe Ahmes (c. 1680–1620 BC), contains the following problem related to trigonometry:[2]"If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?"Ahmes' solution to the problem is the ratio of half the side of the base of the pyramid to its height, or the run-to-rise ratio of its face. In other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face.[2]
Greek mathematics
The chord of an angle subtends the arc of the angle.
Ancient Greek and Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle. One half of the bisected chord is the sine of the bisected angle, that is,
and consequently the sine function is also known as the "half-chord". Due to this
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".[6]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.[2] Based on one interpretation of the Plimpton 322 cuneiform tablet (c. 1900 BC), some have even asserted that the ancient Babylonians had a table of secants.[7] There is, however, much debate as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table.The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.[2] The Rhind Mathematical Papyrus, written by the Egyptian scribe Ahmes (c. 1680–1620 BC), contains the following problem related to trigonometry:[2]"If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?"Ahmes' solution to the problem is the ratio of half the side of the base of the pyramid to its height, or the run-to-rise ratio of its face. In other words, the quantity he found for the seked is the cotangent of the angle to the base of the pyramid and its face.[2]
Greek mathematics
The chord of an angle subtends the arc of the angle.
Ancient Greek and Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle. One half of the bisected chord is the sine of the bisected angle, that is,
and consequently the sine function is also known as the "half-chord". Due to this