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Little is known of Hipparchus's life, but he is known to have been born in Nicaea in Bithynia. Only one work by Hipparchus has survived, and this is certainly not one of his major works. Most of the information which we have about the work of Hipparchus comes from Ptolemy.
Even if he did not invent it, Hipparchus is the first person whose systematic use of trigonometry we have documentary evidence. Hipparchus produced a table of chords, an early example of a trigonometric table. He did this by using the supplementary angle theorem, half angle formulas, and linear interpolation. Hipparchus was not only the founder of trigonometry but also the man who transformed Greek astronomy from a purely theoretical into a practical predictive science. He also introduced the division of a circle into 360 degrees into Greece.
Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. We believe that Hipparchus's star catalogue contained about 850 stars, probably not listed in a systematic coordinate system but using various different ways to designate the position of a star.
The work we have of his, Commentary on Aratus and Eudoxus, was written in 3 books as a commentary on 3 different writings. First, there was a treatise by Eudoxus now lost in which he named and described the constellations. Second, Aratus wrote a poem called which was based on the treatise by Eudoxus and proved to be a work of great popularity. This poem has survived and we have its text. Third, there was commentary on Aratus by Attalus of Rhodes, written shortly before the time of Hipparchus.
The 3 books on which Hipparchus was writing a commentary contained no mathematical astronomy. However towards the end of the second book, continuing through the whole of the third book, Hipparchus gives his own account of the rising and setting of the constellations. Towards the end of the third book, Hipparchus gives a list of bright stars always visible for the purpose of enabling the time at night to be accurately determined. It is thought that this work by Hipparchus was done near the end of his career.
Hipparchus also made a careful study of the motion of the moon. In calculating the distance of the moon, Hipparchus not only made excellent use of both mathematical techniques and observational techniques, but he also gave a range of values within which be calculated that the true distance must lie. He estimated that eclipses have a period of 126007 days. Hipparchus's calculations led him to a value for the distance to the moon of between 59 and 67 earth radii, quite remarkable in that the correct distance is 60 earth radii.
Hipparchus not only gave observational data for the moon which enabled him to compute accurately the various periods, but he developed a theoretical model of the motion of the moon based on epicycles. He showed that his model did not agree totally with observations, but it seems to be Ptolemy who was the first to correct the model to take these discrepancies into account. Hipparchus was also able to give an epicycle model for the motion of the sun, but he did not attempt to give an epicycle model for the motion of the planets.
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How did the astronomy of Hipparchus and Ptolemy violate the principles of Plato and Aristotle?
He was the first person to explain why the sun and stars move across the sky
Who invented longitude and latitude?
Hipparchus (c. 190 BCE - c. 120 BCE) was a Greek astronomer, geographer, and mathematician. The appearance of a nova in the constellation Scorpius inspired him to investigate how stars are born and die. With only the power of his eyes, he created the first accurate star map, a catalogue of 1,080 stars, giving their position and relative brightness. In comparing his chart with one compiled by Timocharis and Aristyllus of Alexandria 150 years earlier, Hipparchus discovered that the earth's axis is precessing, or wobbling, slowly like a top. His calculation of the inclination of the ecliptic, its equation, and his estimate of the annual precession of the equinoxes were all remarkably accurate. He determined the perigee and mean motion of the sun and of the moon, and he calculated the extent of the shifting of the plane of the Moon's motion. Hipparchus' star catalogue was used for over 1600 years, and his system of star magnitudes is still in use. His main contribution to geography was in applying rigorous mathematical principles in determining the location of places on the earth's surface, being the first to do so by specifying a position's latitude and longitude. In the Almagest, Ptolemy made use of a catalogue of stars, whose position Hipparchus had fixed by calculating celestial angular measurements, corresponding to latitude and longitude on earth. Recognizing that the earth was round, he constructed the first globe and was the first to divide a circle into 360 degrees. Hipparchus invented an improved type of astrolabe, which he used to determine accurately the celestial coordinates of stars and a planisphere that allowed stereographic projections (also invented by Hipparchus), making it possible to tell time at night from stellar projections. He calculated the length of the year as 365.24667 days, correct to within 6.5 minutes and by making observations of eclipses, found the distance to the Moon. It isn't known who discovered that the noontime shadow of an upright rod (called a gnomon, derived from the Greek word for "one who knows or examines") is longest at the winter solstice and shortest at the summer solstice. It is known that the Egyptians used the sundial as early as 1500 BCE, and the Greeks learned of it from the Babylonians. The L-shaped figure comprised of the upright rod of a sundial and its shadow is often referred to as a gnomon. By keeping a record of the number of days that elapsed while the shadow of a gnomon passed from its shortest to its greatest length and then back to its shortest length, ancient people learned to measure the length of the year. Hipparchus was born in Nicaea (now Iznik) in Bithynia (now Turkey). He probably spent some years in Alexandria but settled in Rhodes where he made most of his observations. What set him apart from other ancient astronomers was that he collected data based on careful observations and then formed theories to fit the observed facts. Except for a short commentary on an astronomical poem by Arastus, all of Hipparchus works are lost. Most of what is known about him comes from the writings of Strabo of Amaseai (fl. c. CE 21) and Ptolemy's Almagest, written in the 2nd century CE, which was based on Hipparchus' findings. Hipparchus' contributions to astronomy were the most important before the time of Copernicus in the early sixteenth century. Most scientific historians credit Hipparchus with founding trigonometry. The word is derived from two Greek words, trigonum, meaning "triangle," and metron, meaning, "measure," combining to mean "measurement of triangles." In ancient times there was no name for trigonometry, which was not considered a branch of mathematics, merely a collection of techniques and formulas ancillary to astronomy. Hipparchus introduced trigonometric functions in the form of a table of chord arcs used to solve the problem of the computation of specific positions from geometric models. This table is practically the same as that of natural sines. It is likely that he had some means of solving triangles in spherical trigonometry. It is also suspected that Ptolemy's Theorem, which gives the necessary and sufficient conditions that a convex quadrilateral be inscribable in a circle, is due to Hipparchus. The theorem implicitly gives formulas for the sines and cosines of the sum and difference of angles, from which all trigonometric relations can be deduced. Quotation of the Day: "Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." - T. L. Heath [The time the professor alluded to must have been 9:36 p.m. A quarter of the time since noon is 2 hr. 24 min., and a half of the time till noon the next day is 7 hr. 12 min. Together these give us 9 hr. 36 min. This is the answer to the puzzle, but how was the solution found?]
This astronomer is credited with opening the door to the era of modern astronomy?
The earliest recorded heliocentric ("Sun-centered") model of the solar system is generally attributed to Aristarchus of Samos in the 3rd century BC although several philosophers and mystics of many traditions and cultures hypothesized this possibility before and after him. The idea itself is counterintuitive and the geocentric ("Earth centered"), or Ptolemaic view was favored by most astronomers until well into the 17th century.It was Nicolaus Copernicus who first proposed a mathematical model of the solar system with the Sun at the center but his work was not widely known at its publishing and his model was not as accurate at predicting the locations of the planets as the (later proven incorrect) Ptolemaic model.Galileo Galilei was an astronomer of the Copernican school who made important observations of the phases of Venus which proved conclusively that the Ptolemaic system was incorrect. Coupled with his discovery of moons orbiting Jupiter, the case against a geocentric universe was basically insurmountable.Johannes Kepler, a contemporary of Galileo, created a mathematical model of a heliocentric solar system which could be used to make predictions of the locations of the planets with a high degree of accuracy that was missing from the Copernican model.While there is no one father of modern astronomy, Copernicus, Galileo and Kepler are the most often referred to Renaissance astronomers who are responsible for the heliocentric model which represents an incredibly important, fundamental and undeniable shift in the way we all view the universe and our place within it.In the 8th century, Ja'far al-Sadiq refuted the geocentric model of the universe common at the time, in which the Earth is not moving and the Sun, Moon and the planets are orbiting around it. He was the first to refute Ptolemy's theory of the sun having two movements, one going round the Earth in one year and the other going round the earth in 24 hours causing day and night. Al-Sadiq argued that if the Sun is moving round the Earth for one year, it cannot suddenly change its course and go round the Earth for one day. He suggested that this could be explained with a heliocentric theory in which the Earth rotates on its axis and around the Sun. Al-Sadiq also wrote a theory on how the universe is expanding and contracting. He also stated that every object in the universe is always in motion, including objects which appear to be inanimate.[5]Al-Sadiq's student, Geber (Jabir ibn Hayyan), asked him the following question on the stars:"How does the movement of the stars keep them from falling?"[5]Al-Sadiq replied:"Put a stone in a sling and swing it round your head. The stone will stay in the sling so long as you are rotating it. But as soon as you stop the rotation, the stone will fall down on the ground. In the same way the perpetual motion of stars keeps them from falling down."[5]
Brief history of trigonometry?
Trigonometry was probably developed for use in sailing as a navigation method used with astronomy.[2] The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago.[citation needed] The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian's base sixty system of numeration. The Sulba Sutras written in India, between 800 BC and 500 BC, correctly computes the sine of (=45°) as in a procedure for "circling the square" (i.e., constructing the inscribed circle).[citation needed] The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus[1] circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD. The ancient Sinhalese in Sri Lanka, when constructing reservoirs in the Anuradhapura kingdom, used trigonometry to calculate the gradient of the water flow. Archeological research also provides evidence of trigonometry used in other unique hydrological structures dating back to 4 BC.[3] The Indian mathematician Aryabhata in 499, gave tables of half chords which are now known as sine tables, along with cosine tables. He used zya for sine, kotizya for cosine, and otkram zya for inverse sine, and also introduced the versine. Another Indian mathematician, Brahmagupta in 628, used an interpolation formula to compute values of sines, up to the second order of the Newton-Stirling interpolation formula. In the 10th century, the Persian mathematician and astronomer Abul Wáfa introduced the tangent function and improved methods of calculating trigonometry tables. He established the angle addition identities, e.g. sin (a + b), and discovered the sine formula for spherical geometry: Also in the late 10th and early 11th centuries, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the formula . Indian mathematicians were the pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha (circa 1350-1200 BC) is the first person thought to have used geometry and trigonometry for astronomy, in his Vedanga Jyotisha. Persian mathematician Omar Khayyám (1048-1131) combined trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. Khayyam solved the cubic equation x3 + 200x = 20x2 + 2000 and found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables. Detailed methods for constructing a table of sines for any angle were given by the Indian mathematician Bhaskara in 1150, along with some sine and cosine formulae. Bhaskara also developed spherical trigonometry. The 13th century Persian mathematician Nasir al-Din Tusi, along with Bhaskara, was probably the first to treat trigonometry as a distinct mathematical discipline. Nasir al-Din Tusi in his Treatise on the Quadrilateral was the first to list the six distinct cases of a right angled triangle in spherical trigonometry. In the 14th century, Persian mathematician al-Kashi and Timurid mathematician Ulugh Beg (grandson of Timur) produced tables of trigonometric functions as part of their studies of astronomy. The mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in 1595 which may have coined the word "trigonometry".
What is hipparchus full name?
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What has the author Hipparchus written?
Hipparchus has written: 'The geographical fragments of Hipparchus' -- subject(s): Ancient Geography
Who was Hipparchus's family?
The Hipparchus's family is a mysterious family.
What was Hipparchus was best known for his?
Hipparchus was best known for star catalog..
Did hipparchus go to school?
Not a lot is known about Hipparchus, including where and how he was educated, and of he went to school.
What hipparchus was best known for?
Hipparchus was best known for many things. One of them, he invented trigonometry.
Who is the father of trignometry?
Hipparchus
Who was the founder of trigonometry?
hipparchus
Did hipparchus get married?
single
Did hipparchus have a family?
There is limited information about the personal life of Hipparchus, an ancient Greek astronomer. It is believed that he had a daughter, but not much is known about his family beyond that. Hipparchus is primarily known for his significant contributions to the field of astronomy.
Who isthe father of trigonometry?
hipparchus
History of the father of trigonometry?
Hipparchus
