Important figures in History
Anaxagoras of Clazomenae - 500-428 B.C.
Anaxagoras of Clazomenae lived in Athens during the early Greek period. He made many contributions to science, including many correct assumptions dealing with astronomy. When some of his theories contradicted Greek religion, he was put in jail, where he became (according to Plutarch, the great Greek historian) the first known individual to attempt to square the circle.
Antiphon was a Sophist philosopher who discovered the principle of exhaustion, in which a series of increasingly complex regular polygons are inscribed in a circle. This process, though improved upon many times, was used for about two thousand more years.
Hippias of Elis
Hippias of Elis lived in Athens during the 400's B.C. He created a curve called a trisectrix or quadratrix, depending on its use (either trisecting angles or squaring a circle). Hippias' quadratrix, as it is called, could indeed be used to square the circle, but it required an infinite number of steps to do it.
Euclid had an immense impact on geometry. A mathematician at the University of Alexandria, Egypt, Euclid wrote a textbook, called Elements, that would set the logical basis of geometry for the coming centuries. This text was based on five postulates (assumptions) by which all of Euclid's various theorems were proven. While Euclid did not discover all of the theorems in his book, he organized them into a solid structure that facilitated a logical approach to geometry as a whole.
Archimedes of Syracuse - 287-212 B.C.
Archimedes of Syracuse lived most of his life in the Greek city of Syracuse, on the island of Siciliy. He studied at the University of Alexandria at near the same period of Euclid's employment there, and the fact that his father was an astronomer gave him interest in science. As well as making important discoveries in the scientific areas of buoyancy and mechanical advantage, Archimedes did much work in solid geometry (finding the volumes of segments of spheres as well as other three-dimensional shapes). In his work On the Measurement of the Circle he described a method for finding increasingly accurate upper and lower bounds for π by exhaustion in a way similar to Antiphon's. He also used the Archimedian Spiral as another method to square the circle.
Leonardo of Pisa (Fibonacci) - 1180-1250 B.C.
Fibonacci, using new Arabic numerals, wrote a textbook on algebra, also an Arab discovery. He discovered the Fibonacci sequence of numbers (1,1,2,3,5,8,13,21,…) as well. Using Archimedes' method with better square root methods, he improved Archimedes' value of π.
Nicolas Copernicus - 1473-1543
Copernicus, aside from promoting the heliocentric theory of the solar system, first used the secant, a trigonometric function. He was also the first to calculate a table of trigonometric functions for use in his astronomical calculations.
François Viète - 1540-1603
François Viète was a French lawyer who introduced many new terms into the language of mathematics. He found the first formula for π based on an infinite sequence of algebraic operations. This was based partly on Archimedes' method. Viète also found the value of π to 9 decimal places.
Leonardo Da Vinci - 1452-1519
Leonardo Da Vinci recorded in his lengthy journals two methods for squaring the circle. The first rearranged segments of a circle in the form of a parallelogram, the second used the track of a rolling cylinder in order to square the circular base of the cylinder.
Willebrord Snellius - 1580-1626
Willebrord Snellius was a Dutch professor at the University of Leyden. He is known in physics for his work in optics (which incidentally involves trigonometry). By modifying Archimedes' method, he was able to obtain closer bounds for the value of π.
James Gregory - 1638-1675
James Gregory was a Scottish mathematician who found the first infinite series for finding π. This formula, which makes use of arctan and other trigonometric functions, can be seen in the Finding π applet on this site.
John Machin - 1680-1752
John Machin was an English professor of astronomy. In 1706 he developed an expression for π that allowed speedy digit calculations, with which he calculated π to100 decimal places.
Leonhard Euler - 1707-1783
Euler was probably the most prolific mathematical writer ever. Born in Switzerland, he lived in both Russia and Prussia as an eminent member of their respective academic centers. He eventually wrote 886 books as well as many letters. The theorems and proofs that he discovered stretched into every branch of mathematics. Euler found many expressions involving π, including one for π squared, the logarithm of π, and a formula for calculating π that is the fastest known.