geometry

Eratosthenes and the Circumference of the Earth

Eratosthenes and the Circumference of the Earth

Eratosthenes of Cyrene was a Greek mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. He is best known for being the first person to calculate the circumference of the Earth. “Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun the…
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Jean-Victor Poncelet and Projective Geometry

Jean-Victor Poncelet and Projective Geometry

On July 1, 1788, French engineer and mathematician Jean-Victor Poncelet was born, whose study of the pole and polar lines associated with conic led to the principle of duality. As a mathematician, his most notable work was in projective geometry. He developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These discoveries led to…
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Read Euler, he is the Master of us all…

Read Euler, he is the Master of us all…

On September 18, 1783, Swiss mathematician and physicist Leonhard Euler passed away. Euler is considered to be the pre-eminent mathematician of the 18th century and one of the greatest mathematicians to have ever lived. He is also one of the most prolific mathematicians. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis,…
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Bernhard Riemann’s innovative approaches to Geometry

Bernhard Riemann’s innovative approaches to Geometry

On September 17, 1826, influential German mathematician Bernhard Riemann was born. Riemann‘s profound and novel approaches to the study of geometry laid the mathematical foundation for Albert Einstein’s theory of relativity. He also made important contributions to the theory of functions, complex analysis, and number theory. “Nevertheless, it remains conceivable that the measure relations of space in the infinitely small are not in accordance with the assumptions of our geometry [Euclidean geometry],…
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Giovanni Saccheri and his Problems with Euclidian Geometry

Giovanni Saccheri and his Problems with Euclidian Geometry

On September 5, 1667, Italian Jesuit priest, scholastic philosopher, and mathematician Giovanni Girolamo Saccheri was born. He is primarily known today for his last publication, Euclide Ab Omni Naevo Vindicatus (Euclid Freed of Every Flaw, 1733), now considered the second work in non-Euclidean geometry. First Contact with Euclid’s Elements Saccheri was born in Sanremo to his father Giovanni Felice Saccheri, a lawyer and notary.[6] As a child Saccheri ‘was notably precocious’.[1] He entered the…
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Felix Klein and the Klein-Bottle

Felix Klein and the Klein-Bottle

On April 25, 1849, German mathematician and mathematics educator Felix Klein was born. Klein is known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day. Klein also devised the Klein-bottle, a one-sided surface which, if traveled upon, could…
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Number Theory, Topology, and Fractals with Wacław Sierpiński

Number Theory, Topology, and Fractals with Wacław Sierpiński

On March 14, 1882, Polish mathematician Wacław Franciszek Sierpiński was born. Sierpiński is known for contributions to set theory, research on the axiom of choice and the continuum hypothesis, number theory, theory of functions and topology. Three well-known fractals are named after him (the Sierpiński triangle, the Sierpiński carpet and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem. Wacław Sierpiński – Early Years in Russian occupied Poland Wacław…
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Nikolai Lobachevsky – The Copernicus of Geometry

Nikolai Lobachevsky – The Copernicus of Geometry

On February 24, 1856, Russian mathematician and geometer Nikolai Ivanovich Lobachevsky passed away. He is known primarily for his work on hyperbolic geometry. Lobachevsky’s main achievement is the development (independently from János Bolyai) of a non-Euclidean geometry, also referred to as Lobachevskian geometry. Nikolai Lobachevsky – Early Years Nikolai Lobachevsky was born as one of three children either in or near the city of Nizhny Novgorod in Russia in 1792 to parents…
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Janos Bolyai and the Discovery of Non-Euclidian Geometry

Janos Bolyai and the Discovery of Non-Euclidian Geometry

On December 15, 1802, Hungarian mathematician János Bolyai was born. He is most famous for being one of the founders of non-euclidian geometry, a geometry that differs from Euclidean geometry in its definition of parallel lines. János Bolyai – Background Bolyai was born in the Transylvanian town of Kolozsvár (Klausenburg), then part of the Habsburg Empire (now Cluj-Napoca in Romania), the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai. Farkas…
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Gerardus Mercator – The Man who Mapped the Planet

Gerardus Mercator – The Man who Mapped the Planet

On December 2, 1594, German cartographer, philosopher and mathematician Gerardus Mercator passed away. He is best known for his work in cartography, particular the world map of 1569 based on a new projection which represented sailing courses of constant bearing as straight lines. He was the first to use the term Atlas for a collection of maps. “Since my youth geography has been for me the primary object of study. When I…
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