π is the mysterious number that most people think is merely 3.14. π is the ratio of a circle’s circumference to its diameter. π has been calculated to 206,158,430,000 digits, which was accomplished by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo in September of 1999. On the other hand, there were the Babylonians and Hebrews who lived and died, believing that π was simply 3. Evidence from the Rhind papyrus shows that the Egyptians knew 3.16, but implied in their Great Pyramid is the even better value 3.14. Much like the Babylonians, the early Hindus and Chinese accepted 3. Archimedes led the Greeks to believe that the limits of π were 3.141< π <3.143. The later Greeks, with the knowledge of Ptolemy, knew 3.1416. In the 5th century A.D. Tsu Ch’ung-chih, a Chinese mechanician, gave π correct to six decimals. This feat was not paralleled in the western world for 1000 years. Another common belief was that Π was the square root of ten, which was somehow equal to 3 1/7.
A little known verse from the Old Testament leads us to believe that the Hebrews used 3 as their value of Pi. “And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about, (I Kings 7, 23).” There is some speculation involved in this passage, as some say that the diameter of ten cubits was the measurement from one side to the next, whereas the thirty-cubit circumference was of the inner lining of the vessel. If the sides were about 0.2254 cubits thick, this would lead to decent value of pi.
Around 225 B.C., Archimedes obtained his incredibly accurate limits for π with the perimeters of inscribed and circumscribed polygons having 96 sides. This was an extremely difficult task for Archimedes, as he didn’t have Arabic numerals to work with. Lacking Arabic numerals, he had much difficulty in computing the essential square roots square roots. Tsu Ch’ung-chih’s method is not known for sure, but may have been similar to Archimedes’. Following the path of polygon usage, in 1579 Francois Vieta used polygons of 393,216 sides to obtain π to 9 correct places. This style came to an end in 1610, when the German eccentric Ludolph van Ceulen calculated π to 35 places by means of a polygon with 4 quintillion, 611 quadrillion, 686 trillion, 18 billion, 427 million, 387 thousand, 904 sides.
Considering the Greeks had to account for every “supernatural” part of nature, that they could not understand, there is an estimation of three hundred
In an earlier section of The Ascent of Man titled “The Music of the Spheres” Bronowski taught us more about numbers and their origin in the section that states:
It was once said by Johannes Kepler that “Geometry has two great treasures: one is the Theorem of Pythagoras, and the other the division of a line into extreme and mean ratio. Golden Ratio is found by dividing a line into two parts so that the longer part divided by the smaller part equals the whole length divided by the longer part. It is also known as the extreme and mean ratio. Golden ratio is very similar to Pi because it is an infinite number and it goes on forever. It is usually rounded to around 1.618. The formula for golden ratio is a/b = (a+b)/b. Golden Ratio is a number that has been around for many years. It has been around for a long time so it is not known who formed the idea of the golden ratio. Since the golden ratio is used all around the world, it is known in many names such as the golden mean, phi, the divine proportion, extreme and mean proportion, etc. It is usually referred to as phi. Golden ratio was used in arts from the beginning of people and still is used today. It has been used in architecture, math, sculptures and nature. Many famous artists used the golden ratio. Golden ratio can also be used on a rectangle which is known as the golden rectangle. Euclid talks about it in his book Elements. Golden ratio also has a relationship with both the Fibonacci numbers and Lucas numbers.
A little info: Archimedes was a Greek Mathematician who was born in 287 BC and died in 212 BC. He was born in Syracuse, Sicily; during this time, the city was an independent Greek city-state which held a 500-year history. At the Siege of Syracuse Romans at the siege were specifically ordered not to harm Archimedes but he later was pronounced dead by being stabbed by a Roman soldier. His father (Phidias) was an astronomer and is believed to be related to the King of Syracuse. This information was found in his work “The Sand Reckoner.” Archimedes was labeled as one of the top scientists in classical antiquity. In those times, when blackboards and paper were not yet around, Archimedes constructed ashes, dust or all any available surface to help sketch his geometric figures. It’s been told that he used to get so intrigued with all of the work he did that sometimes he forgot to eat, skipped a meal or two just to finish on the project. He was considered the greatest mathematician in antiquity and possibly the greatest of all time.
The Aztecs used body parts to measure. For example if you stretched out your left arm that would be the measure from your heart to the tip of your finger. Puzzling is a system that they use to record areas. Their number system was base 20 so it went 1,20,400,8000.
Squaring the circle with a compass and straightedge had been a problem that puzzled geometers for years. In his notes under the drawing he recognized that “if you open your legs enough that your head is lowered by one-fourteenth of your height and raise your hands enough that your extended fingers touch the line of the top of your head, know that the centre of the extended limbs will be the navel, and the space between the legs will be an equilateral triangle” . This excerpt alone shows that Da Vinci had an immense understanding of proportion, as well as geometry. On this page, Da Vinci also wrote the exact proportions that he used, based his own observations and the ones used in Vitruvius’s book. Da Vinci
Pi, short for Piscine, meaning a rational source of water, is a rational man living in the irrational world, who believes in not one, but three religions, which some may say is irrational. Pi, whose family owned a zoo, faced many hardships
» Part 1 Logarithms initially originated in an early form along with logarithm tables published by the Augustinian Monk Michael Stifel when he published ’Arithmetica integra’ in 1544. In the same publication, Stifel also became the first person to use the word ‘exponent’ and the first to indicate multiplication without the use of a symbol. In addition to mathematical findings, he also later anonymously published his prediction that at 8:00am on the 19th of October 1533, the world would end and it would be judgement day. However the Scottish astronomer, physicist, mathematician and astrologer John Napier is more famously known as the person who discovered them due to his work in 1614 called ‘Mirifici Logarithmorum Canonis Descriptio’.
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
The Greeks were able to a lot of things with only a compass and a straight edge (although these were not their sole tools, the Greeks in fact had access to a wide variety of tools as they were a fairly modern society). For example, they found means to construct parallel lines, to bisect angles, to construct various polygons, and to construct squares of equal or twice the area of a given polygon. However, three constructions that they failed to achieve with only those two tools were trisecting the angle, doubling the cube, and squaring the circle.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes (“Letters”). Although not very important to the development of algebra, Archimedes (212BC – 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics (“Archimedes”).
The twenty first greek letter, Phi, is used to represent the Golden Ratio. The ratio is found by dividing an area into two parts; a and b. “a” and “b” are never equal. The ratio of the entire length of the area to the longer portion is equal to the ratio of the longer portion to the smaller part. The ratio that is formed is irrational and is usually rounded to 1.168 or 0.618. In other words, a/b=(a+b)/a=1.6180339887… Throughout history, this ratio is thought of to be the most pleasing to the eye and artists use it often to enhance details and make proportions look more realistic.
They constructed the 12-month calendar which they based on the cycles of the moon. Other than that, they also created a mathematical system based on the number 60 which they called the Sexagesimal. Though, our mathematics today is not based on their system it acts like a foundation for some mathematicians. They also used the basic mathematics- addition, subtraction, multiplication and division, in keeping track of their records- one of their contributions to this world, bookkeeping. It was also suggested that they even discovered the number of the pi for they knew how to solve the circumference of the circle (Atif, 2013).
from his tables, which showed powers of 10 with a fixed number used as a base.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...