You can observe all of the stars from the equator over the course of a year, although high- declination stars will be difficult to see so close to the horizon. Calendars were often based on the phases of the moon (the origin of the word month) and the seasons. Using the visually identical sizes of the solar and lunar discs, and observations of Earths shadow during lunar eclipses, Hipparchus found a relationship between the lunar and solar distances that enabled him to calculate that the Moons mean distance from Earth is approximately 63 times Earths radius. Chapront J., Touze M. Chapront, Francou G. (2002): Duke D.W. (2002). He was intellectually honest about this discrepancy, and probably realized that especially the first method is very sensitive to the accuracy of the observations and parameters. In any case the work started by Hipparchus has had a lasting heritage, and was much later updated by al-Sufi (964) and Copernicus (1543). The earlier study's M found that Hipparchus did not adopt 26 June solstices until 146 BC, when he founded the orbit of the Sun which Ptolemy later adopted. 3550jl1016a Vs 3550jl1017a . Posted at 20:22h in chesapeake bay crater size by code radio police gta city rp. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. Not much is known about the life of Hipp archus. The armillary sphere was probably invented only latermaybe by Ptolemy only 265 years after Hipparchus. [35] It was total in the region of the Hellespont (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita Libri VIII.2. "The Chord Table of Hipparchus and the Early History of Greek Trigonometry. However, by comparing his own observations of solstices with observations made in the 5th and 3rd centuries bce, Hipparchus succeeded in obtaining an estimate of the tropical year that was only six minutes too long. His contribution was to discover a method of using the . MENELAUS OF ALEXANDRIA (fl.Alexandria and Rome, a.d. 100) geometry, trigonometry, astronomy.. Ptolemy records that Menelaus made two astronomical observations at Rome in the first year of the reign of Trajan, that is, a.d. 98. how did hipparchus discover trigonometry 29 Jun. "The Size of the Lunar Epicycle According to Hipparchus. ?, Aristarkhos ho Samios; c. 310 c. . Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. Input the numbers into the arc-length formula, Enter 0.00977 radians for the radian measure and 2,160 for the arc length: 2,160 = 0.00977 x r. Divide each side by 0.00977. Therefore, his globe was mounted in a horizontal plane and had a meridian ring with a scale. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geographia 1 January 2012). Apparently his commentary Against the Geography of Eratosthenes was similarly unforgiving of loose and inconsistent reasoning. Hipparchus was the very first Greek astronomer to devise quantitative and precise models of the Sun and Moon's movements. Hipparchus must have used a better approximation for than the one from Archimedes of between 3+1071 (3.14085) and 3+17 (3.14286). Swerdlow N.M. (1969). [12] Hipparchus also made a list of his major works that apparently mentioned about fourteen books, but which is only known from references by later authors. Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. Bianchetti S. (2001). The Greeks were mostly concerned with the sky and the heavens. Previously, Eudoxus of Cnidus in the fourth centuryBC had described the stars and constellations in two books called Phaenomena and Entropon. How did Hipparchus discover a Nova? [47] Although the Almagest star catalogue is based upon Hipparchus's one, it is not only a blind copy but enriched, enhanced, and thus (at least partially) re-observed.[15]. ", Toomer G.J. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. Alternate titles: Hipparchos, Hipparchus of Bithynia, Professor of Classics, University of Toronto. [note 1] What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within a tight range of only approximately 12 hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million. [64], The Astronomers Monument at the Griffith Observatory in Los Angeles, California, United States features a relief of Hipparchus as one of six of the greatest astronomers of all time and the only one from Antiquity. Unclear how it may have first been discovered. He is best known for his discovery of the precession of the equinoxes and contributed significantly to the field of astronomy on every level. 1. In calculating latitudes of climata (latitudes correlated with the length of the longest solstitial day), Hipparchus used an unexpectedly accurate value for the obliquity of the ecliptic, 2340' (the actual value in the second half of the second centuryBC was approximately 2343'), whereas all other ancient authors knew only a roughly rounded value 24, and even Ptolemy used a less accurate value, 2351'.[53]. Hipparchus produced a table of chords, an early example of a trigonometric table. UNSW scientists have discovered the purpose of a famous 3700-year-old Babylonian clay tablet, revealing it is the world's oldest and most accurate trigonometric table. (1934). Our editors will review what youve submitted and determine whether to revise the article. (See animation.). Most of our knowledge of it comes from Strabo, according to whom Hipparchus thoroughly and often unfairly criticized Eratosthenes, mainly for internal contradictions and inaccuracy in determining positions of geographical localities. Did Hipparchus invent trigonometry? Hipparchus's catalogue is reported in Roman times to have enlisted about 850 stars but Ptolemy's catalogue has 1025 stars. See [Toomer 1974] for a more detailed discussion. These models, which assumed that the apparent irregular motion was produced by compounding two or more uniform circular motions, were probably familiar to Greek astronomers well before Hipparchus. The Chaldeans also knew that 251 synodic months 269 anomalistic months. He also might have developed and used the theorem called Ptolemy's theorem; this was proved by Ptolemy in his Almagest (I.10) (and later extended by Carnot). The first proof we have is that of Ptolemy. This claim is highly exaggerated because it applies modern standards of citation to an ancient author. Before Hipparchus, astronomers knew that the lengths of the seasons are not equal. Hipparchus produced a table of chords, an early example of a trigonometric table. Diller A. [15][40] He probably marked them as a unit on his celestial globe but the instrumentation for his observations is unknown.[15]. How did Hipparchus discover and measure the precession of the equinoxes? The two points at which the ecliptic and the equatorial plane intersect, known as the vernal and autumnal equinoxes, and the two points of the ecliptic farthest north and south from the equatorial plane, known as the summer and winter solstices, divide the ecliptic into four equal parts. [56] Actually, it has been even shown that the Farnese globe shows constellations in the Aratean tradition and deviates from the constellations in mathematical astronomy that is used by Hipparchus. of trigonometry. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Hipparchus's draconitic lunar motion cannot be solved by the lunar-four arguments sometimes proposed to explain his anomalistic motion. Aubrey Diller has shown that the clima calculations that Strabo preserved from Hipparchus could have been performed by spherical trigonometry using the only accurate obliquity known to have been used by ancient astronomers, 2340. And the same individual attempted, what might seem presumptuous even in a deity, viz. He may have discussed these things in Per ts kat pltos mniaas ts selns kinses ("On the monthly motion of the Moon in latitude"), a work mentioned in the Suda. Not only did he make extensive observations of star positions, Hipparchus also computed lunar and solar eclipses, primarily by using trigonometry. Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and is also close to an integer number of years (4,267 moons: 4,573 anomalistic periods: 4,630.53 nodal periods: 4,611.98 lunar orbits: 344.996 years: 344.982 solar orbits: 126,007.003 days: 126,351.985 rotations). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically. Hipparchus of Nicaea was an Ancient Greek astronomer and mathematician. He considered every triangle as being inscribed in a circle, so that each side became a chord. Chords are closely related to sines. From where on Earth could you observe all of the stars during the course of a year? Eratosthenes (3rd century BC), in contrast, used a simpler sexagesimal system dividing a circle into 60 parts. Hipparchus also analyzed the more complicated motion of the Moon in order to construct a theory of eclipses. Such weather calendars (parapgmata), which synchronized the onset of winds, rains, and storms with the astronomical seasons and the risings and settings of the constellations, were produced by many Greek astronomers from at least as early as the 4th century bce. Ptolemy mentions (Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra, to measure the apparent diameter of the Sun and Moon. For other uses, see, Geometry, trigonometry and other mathematical techniques, Distance, parallax, size of the Moon and the Sun, Arguments for and against Hipparchus's star catalog in the Almagest. He was one of the first Greek mathematicians to do this and, in this way, expanded the techniques available to astronomers and geographers. Dovetailing these data suggests Hipparchus extrapolated the 158 BC 26 June solstice from his 145 solstice 12 years later, a procedure that would cause only minuscule error. He was equipped with a trigonometry table. Because the eclipse occurred in the morning, the Moon was not in the meridian, and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. Some of the terms used in this article are described in more detail here. The history of celestial mechanics until Johannes Kepler (15711630) was mostly an elaboration of Hipparchuss model. Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the gnomon, the astrolabe, and the armillary sphere. Hipparchus also tried to measure as precisely as possible the length of the tropical yearthe period for the Sun to complete one passage through the ecliptic. The Moon would move uniformly (with some mean motion in anomaly) on a secondary circular orbit, called an, For the eccentric model, Hipparchus found for the ratio between the radius of the. But the papyrus makes the date 26 June, over a day earlier than the 1991 paper's conclusion for 28 June. 2 - What are two ways in which Aristotle deduced that. Diophantus is known as the father of algebra. [26] Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. In any case, according to Pappus, Hipparchus found that the least distance is 71 (from this eclipse), and the greatest 81 Earth radii. This was presumably found[30] by dividing the 274 years from 432 to 158 BC, into the corresponding interval of 100,077 days and 14+34 hours between Meton's sunrise and Hipparchus's sunset solstices. Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. He communicated with observers at Alexandria in Egypt, who provided him with some times of equinoxes, and probably also with astronomers at Babylon. [51], He was the first to use the grade grid, to determine geographic latitude from star observations, and not only from the Sun's altitude, a method known long before him, and to suggest that geographic longitude could be determined by means of simultaneous observations of lunar eclipses in distant places. So he set the length of the tropical year to 365+14 1300 days (= 365.24666 days = 365days 5hours 55min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6min per year, an hour per decade, and ten hours per century. Hipparchus had good reasons for believing that the Suns path, known as the ecliptic, is a great circle, i.e., that the plane of the ecliptic passes through Earths centre. It is unknown what instrument he used. According to Roman sources, Hipparchus made his measurements with a scientific instrument and he obtained the positions of roughly 850 stars. Recent expert translation and analysis by Anne Tihon of papyrus P. Fouad 267 A has confirmed the 1991 finding cited above that Hipparchus obtained a summer solstice in 158 BC. All thirteen clima figures agree with Diller's proposal. One of his two eclipse trios' solar longitudes are consistent with his having initially adopted inaccurate lengths for spring and summer of 95+34 and 91+14 days. 2 - Why did Copernicus want to develop a completely. How did Hipparchus discover trigonometry? It was based on a circle in which the circumference was divided, in the normal (Babylonian) manner, into 360 degrees of 60 minutes, and the radius was measured in the same units; thus R, the radius, expressed in minutes, is This function is related to the modern sine function (for in degrees) by This would correspond to a parallax of 7, which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2; Tycho Brahe made naked eye observation with an accuracy down to 1). He contemplated various explanationsfor example, that these stars were actually very slowly moving planetsbefore he settled on the essentially correct theory that all the stars made a gradual eastward revolution relative to the equinoxes. La sphre mobile. Hipparchus attempted to explain how the Sun could travel with uniform speed along a regular circular path and yet produce seasons of unequal length. Trigonometry was probably invented by Hipparchus, who compiled a table of the chords of angles and made them available to other scholars. There are a variety of mis-steps[55] in the more ambitious 2005 paper, thus no specialists in the area accept its widely publicized speculation. He actively worked in astronomy between 162 BCE and 127 BCE, dying around. ", Toomer G.J. Hipparchus was born in Nicaea (Greek ), in Bithynia. Part 2 can be found here. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are 360650 = 03314. Even if he did not invent it, Hipparchus is the first person whose systematic use of trigonometry we have documentary evidence. Apparently it was well-known at the time. [15] Right ascensions, for instance, could have been observed with a clock, while angular separations could have been measured with another device. The Greek astronomer Hipparchus, who lived about 120 years BC, has long been regarded as the father of trigonometry, with his "table of chords" on a circle considered . Although Hipparchus strictly distinguishes between "signs" (30 section of the zodiac) and "constellations" in the zodiac, it is highly questionable whether or not he had an instrument to directly observe / measure units on the ecliptic. It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Since the work no longer exists, most everything about it is speculation. Hipparchus was born in Nicaea, Bithynia, and probably died on the island of Rhodes, Greece. Ptolemy has even (since Brahe, 1598) been accused by astronomers of fraud for stating (Syntaxis, book 7, chapter 4) that he observed all 1025 stars: for almost every star he used Hipparchus's data and precessed it to his own epoch 2+23 centuries later by adding 240' to the longitude, using an erroneously small precession constant of 1 per century. To do so, he drew on the observations and maybe mathematical tools amassed by the Babylonian Chaldeans over generations. Ptolemy quotes an equinox timing by Hipparchus (at 24 March 146BC at dawn) that differs by 5 hours from the observation made on Alexandria's large public equatorial ring that same day (at 1 hour before noon): Hipparchus may have visited Alexandria but he did not make his equinox observations there; presumably he was on Rhodes (at nearly the same geographical longitude). However, Strabo's Hipparchus dependent latitudes for this region are at least 1 too high, and Ptolemy appears to copy them, placing Byzantium 2 high in latitude.) Ptolemy quotes (in Almagest III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time. ), Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. Updates? (1973). Etymology. Analysis of Hipparchus's seventeen equinox observations made at Rhodes shows that the mean error in declination is positive seven arc minutes, nearly agreeing with the sum of refraction by air and Swerdlow's parallax. A new study claims the tablet could be one of the oldest contributions to the the study of trigonometry, but some remain skeptical. (1991). The distance to the moon is. Hipparchus, also spelled Hipparchos, (born, Nicaea, Bithynia [now Iznik, Turkey]died after 127 bce, Rhodes? We know very little about the life of Menelaus. Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. . He developed trigonometry and constructed trigonometric tables, and he solved several problems of spherical trigonometry. 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. Hipparchus calculated the length of the year to within 6.5 minutes and discovered the precession of the equinoxes. As a young man in Bithynia, Hipparchus compiled records of local weather patterns throughout the year. This was the basis for the astrolabe. Trigonometry (from Ancient Greek (trgnon) 'triangle', and (mtron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and ratios of lengths. [48], Conclusion: Hipparchus's star catalogue is one of the sources of the Almagest star catalogue but not the only source.[47]. [29] (The maximum angular deviation producible by this geometry is the arcsin of 5+14 divided by 60, or approximately 5 1', a figure that is sometimes therefore quoted as the equivalent of the Moon's equation of the center in the Hipparchan model.). The history of trigonometry and of trigonometric functions sticks to the general lines of the history of math. Most of Hipparchuss adult life, however, seems to have been spent carrying out a program of astronomical observation and research on the island of Rhodes. As with most of his work, Hipparchus's star catalog was adopted and perhaps expanded by Ptolemy. In combination with a grid that divided the celestial equator into 24 hour lines (longitudes equalling our right ascension hours) the instrument allowed him to determine the hours. Before Hipparchus, Meton, Euctemon, and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice) on 27 June 432BC (proleptic Julian calendar). Ptolemy describes the details in the Almagest IV.11. Anyway, Hipparchus found inconsistent results; he later used the ratio of the epicycle model (3122+12: 247+12), which is too small (60: 4;45 sexagesimal). At school we are told that the shape of a right-angled triangle depends upon the other two angles. The shadow cast from a shadow stick was used to . He is also famous for his incidental discovery of the. This is called its anomaly and it repeats with its own period; the anomalistic month. Greek astronomer Hipparchus . Hipparchus made observations of equinox and solstice, and according to Ptolemy (Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 9412 days, and summer (from summer solstice to autumn equinox) 92+12 days. How did Hipparchus discover trigonometry? With Hipparchuss mathematical model one could calculate not only the Suns orbital location on any date, but also its position as seen from Earth. I. Hipparchus must have been the first to be able to do this. Trigonometry is discovered by an ancient greek mathematician Hipparchus in the 2 n d century BC. This was the basis for the astrolabe. View three larger pictures Biography Little is known of Hipparchus's life, but he is known to have been born in Nicaea in Bithynia. Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the ecliptic, or to take account of the lunar parallax. Knowledge of the rest of his work relies on second-hand reports, especially in the great astronomical compendium the Almagest, written by Ptolemy in the 2nd century ce. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars. However, this does not prove or disprove anything because the commentary might be an early work while the magnitude scale could have been introduced later. At the same time he extends the limits of the oikoumene, i.e. He tabulated the chords for angles with increments of 7.5. [18] The obvious main objection is that the early eclipse is unattested, although that is not surprising in itself, and there is no consensus on whether Babylonian observations were recorded this remotely. Isaac Newton and Euler contributed developments to bring trigonometry into the modern age. [52] Hipparchus (/hprks/; Greek: , Hipparkhos; c.190 c.120BC) was a Greek astronomer, geographer, and mathematician. An Investigation of the Ancient Star Catalog. How to Measure the Distance to the Moon Using Trigonometry First, change 0.56 degrees to radians. Trigonometry, which simplifies the mathematics of triangles, making astronomy calculations easier, was probably invented by Hipparchus. The system is so convenient that we still use it today! Hipparchus could draw a triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. 1:28 Solving an Ancient Tablet's Mathematical Mystery Pliny the Elder writes in book II, 2426 of his Natural History:[40]. Ptolemy made no change three centuries later, and expressed lengths for the autumn and winter seasons which were already implicit (as shown, e.g., by A. Aaboe). He is considered the founder of trigonometry,[1] but is most famous for his incidental discovery of the precession of the equinoxes. These must have been only a tiny fraction of Hipparchuss recorded observations. [63], Jean Baptiste Joseph Delambre, historian of astronomy, mathematical astronomer and director of the Paris Observatory, in his history of astronomy in the 18th century (1821), considered Hipparchus along with Johannes Kepler and James Bradley the greatest astronomers of all time. Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. Ulugh Beg reobserved all the Hipparchus stars he could see from Samarkand in 1437 to about the same accuracy as Hipparchus's. Hipparchus is credited with the invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus's lunar theory. Hipparchus produced a table of chords, an early example of a trigonometric table. Hipparchus also adopted the Babylonian astronomical cubit unit (Akkadian ammatu, Greek pchys) that was equivalent to 2 or 2.5 ('large cubit'). and for the epicycle model, the ratio between the radius of the deferent and the epicycle: Hipparchus was inspired by a newly emerging star, he doubts on the stability of stellar brightnesses, he observed with appropriate instruments (pluralit is not said that he observed everything with the same instrument). He is considered the founder of trigonometry. In particular, he improved Eratosthenes' values for the latitudes of Athens, Sicily, and southern extremity of India. The historian of science S. Hoffmann found proof that Hipparchus observed the "longitudes" and "latitudes" in different coordinate systems and, thus, with different instrumentation. the radius of the chord table in Ptolemy's Almagest, expressed in 'minutes' instead of 'degrees'generates Hipparchan-like ratios similar to those produced by a 3438 radius. A rigorous treatment requires spherical trigonometry, thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. 104". He did this by using the supplementary angle theorem, half angle formulas, and linear . The random noise is two arc minutes or more nearly one arcminute if rounding is taken into account which approximately agrees with the sharpness of the eye. He did this by using the supplementary angle theorem, half angle formulas, and linear interpolation. Hipparchus's ideas found their reflection in the Geography of Ptolemy. "Geographical Latitudes in Eratosthenes, Hipparchus and Posidonius". 103,049 is the tenth SchrderHipparchus number, which counts the number of ways of adding one or more pairs of parentheses around consecutive subsequences of two or more items in any sequence of ten symbols. At the end of his career, Hipparchus wrote a book entitled Peri eniausou megthous ("On the Length of the Year") regarding his results. He was able to solve the geometry legacy nightclub boston Likes. The papyrus also confirmed that Hipparchus had used Callippic solar motion in 158 BC, a new finding in 1991 but not attested directly until P. Fouad 267 A. This is an indication that Hipparchus's work was known to Chaldeans.[32]. He was an outspoken advocate of the truth, of scientific . It remained, however, for Ptolemy (127145 ce) to finish fashioning a fully predictive lunar model. [65], Johannes Kepler had great respect for Tycho Brahe's methods and the accuracy of his observations, and considered him to be the new Hipparchus, who would provide the foundation for a restoration of the science of astronomy.[66]. What is Aristarchus full name? In the practical part of his work, the so-called "table of climata", Hipparchus listed latitudes for several tens of localities. Hipparchus was an ancient Greek polymath whose wide-ranging interests include geography, astronomy, and mathematics. Every year the Sun traces out a circular path in a west-to-east direction relative to the stars (this is in addition to the apparent daily east-to-west rotation of the celestial sphere around Earth). Toomer, "The Chord Table of Hipparchus" (1973). The globe was virtually reconstructed by a historian of science. The purpose of this table of chords was to give a method for solving triangles which avoided solving each triangle from first principles. Please refer to the appropriate style manual or other sources if you have any questions. It was disputed whether the star catalog in the Almagest is due to Hipparchus, but 19762002 statistical and spatial analyses (by R. R. Newton, Dennis Rawlins, Gerd Grasshoff,[44] Keith Pickering[45] and Dennis Duke[46]) have shown conclusively that the Almagest star catalog is almost entirely Hipparchan. Hipparchus's only preserved work is ("Commentary on the Phaenomena of Eudoxus and Aratus"). This is a highly critical commentary in the form of two books on a popular poem by Aratus based on the work by Eudoxus. While every effort has been made to follow citation style rules, there may be some discrepancies. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201BC, 19 March 200BC, and 11 September 200BC. (1967). How did Hipparchus discover trigonometry? He computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length of 1 arcminute along its perimeter. Hipparchus (/ h p r k s /; Greek: , Hipparkhos; c. 190 - c. 120 BC) was a Greek astronomer, geographer, and mathematician.He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equinoxes. This has led to speculation that Hipparchus knew about enumerative combinatorics, a field of mathematics that developed independently in modern mathematics.
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how did hipparchus discover trigonometry