The history of mathematics stretches back to the ancient Greeks, who developed a numeral system around 450 BCE. The philosopher Thales of Miletus laid the foundation for geometry, and Pythagoras of Samos created the Pythagoras theorem – the mathematical formula for calculating the length of the sides of a right-angled triangle. Pythagoras also devised the formula for the distance between two points. Other ancient Greeks, such as Zeno of Elea, developed an abstract geometry and posed a series of paradoxes related to motion, while Leucippus and Democritus created the atomic theory of indivisible.
Pythagoras
Pythagoras was an ancient Greek philosopher. His teachings stressed immortality, transmigration of the soul, and virtuous behavior toward all living things. The Greek philosopher also promoted the concept of “number” as truth. As a result, mathematics was a major focus of Pythagoras’ life.
The Pythagoreans used geometry to solve equations. One of their most famous inventions was the Tetractys, a triangular structure with five equal sides. The Tetractys also adds to 10 and symbolized the four classical elements: fire, air, and water.
However, there is no definitive proof of how Pythagoras discovered the theorem that bears his name. Some scholars say that Pythagoras discovered the first proof of the theorem in a figure, while others say that his discovery was independently made in several different cultures.
While studying mathematics, Pythagoras also studied other subjects. He was fascinat with the relationship between the length of a string and its pitch. This led him to experiment with different levels of water on a string and discovered that each level represented a different musical note. This work later became the basis of the mathematical theories of René Descartes.
The Pythagoreans are also responsible for discovering the first pair of amicable numbers. An amicable number is any number with divisors that equal each other. For example, 220 and 284 are amicable numbers. If the divisors of 220 are 1 and 4, then the new triangle would be based on the hypotenuse of the first one.
In his writings, Aristotle refers to Pythagoras as “the so-called Pythagoreans,” but in reality, he may never have referred to the Pythagorean. He claims that he collected other men’s writings and derived his wisdom from them. Although he does not mention Pythagoras directly, he does discuss the Pythagorean as a founder.
Despite Pythagoras’ contribution to math, there are many questions about his beliefs. The most significant is whether or not Pythagoras believed in animal sacrifice. Although Pythagoras considered animal sacrifices an inconvenient ritual, he didn’t condemn it. He also didn’t forbid eating some animal foods. However, later tradition has suggested that meat eating and metempsychosis are compatible.
Leonhard Euler
Leonhard Euler, also known as Leopold Euler, was a German mathematician. Although he studied theology, Greek and Hebrew, he was more interested in mathematics. He met Johann Bernoulli in his early 20s, who convinced him that he would be a mathematician. The Prussian king disapproved of Euler’s practical engineering skills, but he continued to work in mathematics. The Prussian king found Euler’s mathematicians unsophisticated and expressed disappointment, but he still produced work in almost every branch of mathematics. In total, Euler published over 800 papers.
After his academic career, Euler focused his efforts on developing an array of mathematical principles. This work laid the foundation for modern mathematics. He was a pioneer in several areas and is considered the inventor of the identity theorem. His work on the laws of motion was primarily concerned with astronomy and lunar motion, but he was also interested in acoustics, mechanics, and other subjects.
In addition to proving the identities of prime numbers, Euler was also the first to use analytic methods for number theory problems. This work led to many breakthroughs in mathematics, including the development of a new branch of mathematics known as analytic number theory. He also invented and generalized Fermat’s little theorem and created a theory of the totient function ph(n). Other discoveries of Euler include proving the infinity of prime numbers, as well as the theory of divisibility and quadratic reciprocity.
Euler was a prolific mathematician who devoted his life to science. His contributions included the development of calculus, geometry, and trigonometry. He published hundreds of articles during his lifetime and even after he lost his sight, he continued to write. He was consider one of the greatest mathematicians of all time.
Euler’s vision declined throughout his mathematical career, causing him to be almost blind in his right eye in 1735. He blamed this on the painstaking cartography work he did in his early life. However, despite his declining eyesight, his mind compensated for the lack of vision by using his photographic memory and mental calculation skills.
Hippasus
The story of Hippasus illustrates the power of surprises in mathematics. While he is best known for revealing the method for building a dodecahedron, the story of how he discovered it is less well known. In fact, his discovery was a closely guarded secret. Many mathematicians who make new discoveries are less likely to hide them and shout them from the rooftops.
Hippasus’ discovery revolutionized Western mathematics. It show that lines and square proportions could not described as simple ratios. In addition, he showed that points and lines would be the common measure of magnitudes. However, these discrete numbers and points would never be able to capture the world in its entirety. This discovery led to the establishment of geometry as a proper science, studying the relationships between continuous magnitudes.
Hippasus’ discovery of irrational numbers gave geometry an advantage over arithmetic. However, this discovery upset the Pythagorean brotherhood. They thought that Hippasus had exposed a secret and went against their beliefs. Hippasus was later drown or killed by his own brother.
Hippasus was also the first to discover the concept of incommensurability. Before him, Pythagoreans believed that any two magnitudes were commensurable. However, Hippasus discovered that the sides and diagonals of a square were not commensurable. This disprove the Pythagorean idea that everything was made up of whole numbers.
Although Hippasus’ discovery was considered groundbreaking, his death remains mysterious. His colleagues wished they’d thrown him overboard, but the story is not entirely true. The story of Hippasus’ death was probably embellished for historical purposes. However, it is possible that his discovery was discovered by a different person.
Al-Karaji
Al-Karaji is credit with being the first person to use induction in mathematics. He used the principle to prove that a binomial was half the product of two preceding numbers. This proved that a binomial could be expand indefinitely. However, his theory was not very useful for solving complex problems.
Al-Karaji was a mathematician who worked in the Islamic world. He was an official under the ruler of Baghdad and wrote a book called “Sufficient” which was use by civil servants. It taught the students how to calculate with integers, find the square root of a number, and determine area and volume of an object. He also wrote a book on more advanced algebra that was titled, “The Glorious and Wonderful”.
During the Renaissance, Persian and Middle Eastern scholars made great contributions to math. In particular, Muhammad ibn Musa Al-kharizmi made many breakthroughs in algebra. He also developed algebraic notation and geometry, which we know today as algebraic calculus. These developments all contributed to the evolution of math in the renaissance.
In the eighth century, the Islamic Empire spanned the Middle East, North Africa, Central Asia, and Persia. This period was also notable for the merging of the mathematical advances of India and Greece. In addition, the prohibition against depicting the human body led to the widespread use of geometric patterns as decoration. Ultimately, this became an art form.
The Arabic mathematicians primarily known for their contributions in the areas of algebra, number theory, and number systems. However, they also made significant contributions to geometry, trigonometry, and mathematical astronomy. Abu’l-Sinan and al-Quhi both contributed to the revival of Greek higher geometry in the Islamic world. They also studied the properties of conic sections and the properties of mirrors.
