First Egyptian pyramids constructed using masterful planning as well as sharp and detailed understanding of geometrical shapes and concepts.
Approx. 2,000 BC
This was the first known instance of someone correctly mapping the area of a triangle with a pre-determined formula in recorded history
Approx. 1800 BC
The Moscow Mathematical Papyrus was a document discovered containing 25 new ideas in mathematical and geometrical history.
Approx. 1650 BC
The Rhind Papyrus was an 18 feet wide document containing 48 new problems revolving mostly around dealing with fractions.
2's Square Root
Baudhayana, author of the Baudhayana Sulba Sutra, a Vedic Sanskrit geometric text, contains quadratic equations, and calculates the square root of 2 correct to five decimal places
The Shatapatha Brahmana
Approx. 700 BC
The Shatapatha Brahmana is a prose text describing Vedic rituals, history and mythology associated with the Śukla Yajurveda.
Brahmagupta's formula: The area, A, of a cyclic quadrilateral with sides of lengths a, b, c, d, respectively, is given by
the other Vedic “Sulba Sutras” (“rule of chords” in Sanskrit) use Pythagorean triples, contain of a number of geometrical proofs, and approximate π at 3.16
Pappus Of Alexandria
Pappus of Alexandria states his hexagon theorem and his centroid theorem
Hipparchus develops the bases of trigonometry.
The Nine Chapters on the Mathematical Art
The Nine Chapters on The Mathematical Art lays out an approach to mathematics that centers on finding the most general methods of solving problems
Thales of Miletus
Approx. 624 BC - Approx. 546 BC
Created and proved Thales Theorem DE/BC=AE/AC=AD/AB
Approx. 570 BC - Approx. 495 BC
Pythagorean theorem is named after him although its not been proven that he ever even existed
Approx. 455 BC
A set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea
Greeks use numerals
Approx. 450 BC
First recorded incident of written numerals in Greece
427 BC - 347 BC
a philosopher that is highly esteemed by the Greeks. There is a story that he had inscribed above the entrance to his famous school, "Let none ignorant of geometry enter here." However, the story is considered to be untrue.
He was NOT a mathematician however his views helped shape many concepts
After Archimedes died hellenistic geometry started to decline in popularity
Approx. 387 BC
Plato founds the Academy in Athens. He identifies five polyhedra now known as Platonic bodies.
Eudoxus Rational and Irrational Comparison
Approx. 360 BC
Eudoxus makes a definition allowing the possibility of using irrational lengths and comparing them with rational lengths by using cross multiplication.
Approx. 325 BC - Approx. 265 BC
Euclid is considered to be one of the three greatest mathematicians of all time. He discovered Euclidean geometry which use his axioms and theorems as they relate to plane and solid figures.
Approx. 300 BC
Euclid writes The Elements, a book discussing Euclidean geometry. The Elements is a collection of 13 books of definitions, postulates, and axioms. It became the 3rd most popular book in the world, after the Koran and the Bible.
Approx. 287 BC - Approx. 212 BC
Archimedes is regarded as the greatest Greek mathematician. He invented 3 simple machines, the pulley, screw, and lever. The Archimedes screw, a device used for raising water, is still in use today. He also analyzed the area of a circle and discovered how to calculate volumes and surface areas of spheres and cylinders.
Volume of a cylinder
Approx. 250 BC
Archimedes discovers the formula for how to calculate the volume of a cylinder.
The Earth's Circumference
Eratosthenes estimates the circumference of the Earth, only missing by about 15%.
Area of an Encircled Quadrilateral
Approx. 628 AD
Brahmagupta created a formula for finding the area of a quadrilateral, with sides a,b,c,d, enclosed by a circle: A = The Sq. Root of (s-a)(s-b)(s-c)(s-d). S is the semi-perimeter, is found by the formula s=(a+b+c+d)/2
Synthesis of Algebra and Geometry
Approx. 853 AD
Modern Age Geometry
1596 - 1650
Descartes synthesized algebra and geometry by placing points on a coordinate plane.
Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
25 December 1643 - 20 March 1727
Widely known as a the man who helped revolutionize the concept of gravity Newton made several contributions to mathematics and geometry as well as science including being credited as one of the fathers of calculus.
Gottfried Wilhelm Leibniz
July 1 1646 - November 14 1716
Leibniz was a German mathematician who is credited as also being a father of modern calculus
Even though there is much controversy surrounding it its widely believed that Sir Isaac Newton and Gottfried Wilhelm Leibniz both discovered/created calculus in the mid 17th century
Carl Friedrich Gauss
1777 - 1855
Gauss developed the Gauss method for adding large amounts of consecutive numbers when he was six. However, his most important creation is that of non-Euclidean geometry. Non-Euclidean geometry is geometry not based on the postulates of Euclid. This includes times when the parallel postulate isn't true. Parallel Postulate - Through a given point not on a line, there is one and only one line parallel to it.
Louis Poinsot discovers the two remaining Kepler-Poinsot polyhedra.
George Friedrich Bernhard Riemann
1826 AD - 1866 AD
Riemann was one of the foremost geometers in the development of Non-Euclidean Geometry. He also was a lecturer at the University of Gottingen
1854 – Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space.
Ferdinand von Lindemann
Ferdinand von Lindemann proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,
Three Cottage Problem Disproved
Casimir Kuratowski shows that the three-cottage problem has no solution
The problem is as follows:
"Suppose there are three cottages on a plane (or sphere) and each needs to be connected to the gas, water, and electricity companies. Without using a third dimension or sending any of the connections through another company or cottage, is there a way to make all nine connections without any of the lines crossing each other?"
The Fractal Geometry Of Nature
In 1982, Benoit Mandelbrot publishing The Fractal Geometry of Nature, a book popularizing fractal geometry. Fractal geometry deals with fractioned dimensions.
Classification of finite simple groups
the classification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed
Mapping of E8
A team of researches throughout North America and Europe used networks of computers to map E8