Hipparchus And The Precession Of The Equinoxes

Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and is best known for the Pythagorean theorem which relates the two sides of a triangle to the hypotenuse using the formula a squared plus b squared equals c squared. However, because legend and obfuscation cloud his work even more than that of other pre-Socratic philosophers, one can give only a tentative account of his teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accomplishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were

Ancient Greek astronomers made some amazing mathematical and philosophical discovers about our universe. From the Hellenistic Greek observations in approximately 300 B.C.E., to the invention of the first telescope in the seventeenth century, to the launching of today’s space probes, one thing is evident: astrological observations are imperative to creating a calendar.

Pythagoras also contributed to the music world. He expressed the musical harmony in formulas. He created a scale layout with gongs in different sizes and he proved that in the resonance of the gongs he hit, 1 octave interval is equal to 2:1 proportion, the perfect fifth is equal to 3:2 proportion, perfect four is equal to 4:3 proportion and whole notes are equal to 9:8. This, later started to be known as “Pythagorean Tuning.”

Johannes Kepler (1571-1630) was a German astronomer who believed in the heliocentric theory. Kepler is a clear example of the narrow line that separated science and religion. Nonetheless, his ideas would show that things could be solved through reason alone. He believed that the harmony of the human soul could be found through numerical relationships that existed between planets. He found that the planets: Mercury, Venus, Earth, Mars, Uranus, Jupiter, and Saturn all revolved at different times. For example, the earth revolved around the sun in a year while Saturn revolved around the sun in fifty years. From this, Kepler found a mathematical ratio, nine to the two-thirds power, to explain this phenomenon. This was revolutionary to humanity’s place in the universe. People were shocked that the universe could be explained by math alone rather than religion. This went strongly

He used logic and reasoning to investigate the nature of the universe. Ptolemy’s model helped get people thinking about the universe being eternal, finite, and spherical. This document is most definitely not reliable because the conclusion was made without having all the needed information, and it was later disproved. A more accurate view could come from someone who does in depth studies of how the universe is actually laid out. As seen in Document 11, A Greek doctor by the name of Hippocrates became one of the first people that taught his belief that illnesses only had

Hipparchus was a greek astronomer, geographer, and mathematician born 190 B.C. in Nicaea and died in 120 B.C. Rhodes, Rhodes, Greece. Hipparchus is accredited as the inventor of trigonometry because of his discovery of the first table of chords and also because he's the only person with valid data of the discovery and usage of trigonometry. In order to calculate the rising and setting of zodiacal signs, Hipparchus brought to light the division of circles into 360 degrees and the calculation of chords by looking at the triangles (spherical triangles or triangles that made up a circle) differently. Hipparchus experimented putting all triangles to be within a circle and with the three points each touching the

His model said that the planets moved not in circles around the sun, but in ellipses and the mathematics was proved using three laws:

One of Thales’ most renounced findings include his discovery in geometric studies in the area reading the rules of triangles. He came to the conclusion that if the base angles of an isosceles triangle are equal, the sum of the angles of a triangle are equivalent to two right angles. With the application of “geometric principles to life situations, Thales was able to calculate the height of a pyramid by measuring its shadow, and the distance of a boat to the shore, by using the concept of similar triangles” (pg. 5, Muehlbauer). Realizations such as these helped shape the beginning for the formation of natural law based on observations of the world through explanation.

(between June 20th and June 22nd) the Greek Astronomer, Eratosthenes had heard of a famous well in a Egyptian City called Syene (now known as Aswan) located around the Nile River. He knew that every year on the solstice, there was no shadow on the bottom of well but instead the rays of sunlight reflected back, and not on the sides of the well as on other days. He came to a conclusion that the sun was directly overhead in Syene at noon every year. He knew that in his hometown Alexindra, the sun was never directly above him even on the solstice. He assembled a pole in Alexindra to study and calculate the shadows position eventually proving that no sun was directly above but faintly south. Knowing that the earth was curved and knowing the distance between the two cities, Syene and Alexandra he calculated the planets circumference by doing simple geometry. “Eratosthenes could measure the angle of the Sun’s rays off the vertical by dividing the length of the leg opposite the angle (the length of the shadow) by the leg adjacent to the angle (the height of the pole). This gave him an angle of 7.12 degrees. He knew that the circumference of Earth constituted a circle of 360 degrees, so 7.12 (or 7.2, to divide 360 evenly by 50) degrees would be about one-fiftieth of the circumference. He also knew the approximate distance between Alexandria and Syene, so he could set up this

The Greeks made several inventions, most notably in the subject of math, which are still studied today and taught in school. Mathematician Euclid is often credited as the “Father of Geometry” for all his work and studies in this subject, which are compiled in his books called The Elements. He organized known geometrical statements called theorems and logically proved all of them. He proved the theorem of Pythagoras (another Greek mathematician), which stated that the equation (c2 = a2 + b2) is true for every right triangle.

In other words Claudius Ptolemy was an astronomer who was born during the year 85 AD . He spent most of his life studying how the Earth, Planets, and Sun moved. He was one of the very first astronomers so, not very much was known. A lot of people doubted him because in his time religion was very important and they thought that they only thing you couldn't see with the naked eye was Heaven and hell. His first time he published his observation was on March 26th 127. He spent almost 20 years getting his theory to make sense. He knew people wouldn't believe him so he broke down his discovery into thirteen books and each book was a part of his discovery. After he published his first one he was able to do a couple small ones, but sadly, the last of his discoveries was made on

Geometry first originated as a way to solve problems in architecture and navigation. A famous figure in geometry is Euclid. Around 300 BC, he published a book, The Elements, which contained definitions, axioms, and postulates that would be regarded as a standard of mathematical reasoning for the next two thousand years (Mueller, 1969). Euclid basically gave the foundation of what is now called Euclidean geometry. However,

The ratio between the time and where the pendulum is confuses people the most. People found the sine factor to be confusing so Foucault made the gyroscope in 1852 to try and help them understand the concept of time with the pendulum. The gyroscope’s spinning rotor tracks the stars directly. Its axis of rotation turns once per day whatever the latitude, unaffected by the sine factor.

Johannes Kepler was a German astronomer and mathematician who lived between 1671-1630. Kepler was a Copernican and initially believed that planets should follow perfectly circular orbits (“Johan Kepler” 1). During this time period, Ptolemy’s geocentric theory of the solar system was accepted. Ptolemy’s theory stated that Earth is at the center of the universe and stationary; closest to Earth is the Moon, and beyond it, expanding towards the outside, are Mercury, Venus, and the Sun in a straight line, followed by Mars, Jupiter, Saturn, and the “fixed stars”. The Ptolemaic system explained the numerous observed motions of the planets as having small spherical orbits called epicycles (“Astronomy” 2). Kepler is best known for introducing three

According to Victor Katz in “A History of Mathematics (3rd Edition)” (Pearson, 2008), trigonometry developed primarily from the needs of Greek and Indian astronomers. But today, trigonometry and geometry were used on various fields such as: architecture, physical sciences, engineering, astronomers, medical imaging (CAT scans and ultrasounds), etc.