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What (who) is E8 (mathematics) - definition
248-DIMENSIONAL EXCEPTIONAL SIMPLE LIE GROUP
E8 (group); E8 (Mathematics); Lie group E8; E8 shape; E₈ (mathematics); E₈; E8 Lie group; E8 Lie algebra
![root poset]] with edge labels identifying added simple root position](https://commons.wikimedia.org/wiki/Special:FilePath/E8HassePoset.svg?width=200 "root poset]] with edge labels identifying added simple root position")
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled G2, F4, E6, E7, and E8.
Mathematics in medieval Islam
![[[Omar Khayyám]]'s "Cubic equations and intersections of conic sections" the first page of the two-chaptered manuscript kept in Tehran University](https://commons.wikimedia.org/wiki/Special:FilePath/Khayyam-paper-1stpage.png?width=200 "[[Omar Khayyám]]'s \"Cubic equations and intersections of conic sections\" the first page of the two-chaptered manuscript kept in Tehran University")
![To solve the third-degree equation ''x''<sup>3</sup> + ''a''<sup>2</sup>''x'' = ''b'' Khayyám constructed the [[parabola]] ''x''<sup>2</sup> = ''ay'', a [[circle]] with diameter ''b''/''a''<sup>2</sup>, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the ''x''-axis.](https://commons.wikimedia.org/wiki/Special:FilePath/Omar Kayyám - Geometric solution to cubic equation.svg?width=200 "To solve the third-degree equation ''x''<sup>3</sup> + ''a''<sup>2</sup>''x'' = ''b'' Khayyám constructed the [[parabola]] ''x''<sup>2</sup> = ''ay'', a [[circle]] with diameter ''b''/''a''<sup>2</sup>, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the ''x''-axis.")
![Engraving of [[Abū Sahl al-Qūhī]]'s perfect compass to draw conic sections.](https://commons.wikimedia.org/wiki/Special:FilePath/Gravure originale du compas parfait par Abū Sahl al-Qūhī.jpg?width=200 "Engraving of [[Abū Sahl al-Qūhī]]'s perfect compass to draw conic sections.")
![theorem of Ibn Haytham]].](https://commons.wikimedia.org/wiki/Special:FilePath/Theorem of al-Haitham.JPG?width=200 "theorem of Ibn Haytham]].")
THE BODY OF MATHEMATICS PRESERVED AND ADVANCED UNDER THE ISLAMIC CIVILIZATION BETWEEN CIRCA 622 AND 1600
Islamic Mathematics; List of Muslim mathematicians; Muslim Mathematicians; Muslim mathematicians; Islamic mathematician; History of mathematics in Islamic culture; Mathematics in the Middle-East; Islamic mathematicians; Arabian mathematics; Arab mathematics; Arabic mathematics; Medieval Islamic Mathematics; Medieval Islamic mathematics; Islamic mathematics; Mathematics in the Islamic Golden Age; Mathematics in the Golden Age of Islam; Mathematics in the Caliphates; Saracenic mathematics; Islamic maths; Islamic geometry; Arabic mathematic; Algebra in medieval Islam; Irrational numbers in medieval Islam; Mathematics in medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.
Mathematics in the medieval Islamic world
THE BODY OF MATHEMATICS PRESERVED AND ADVANCED UNDER THE ISLAMIC CIVILIZATION BETWEEN CIRCA 622 AND 1600
Islamic Mathematics; List of Muslim mathematicians; Muslim Mathematicians; Muslim mathematicians; Islamic mathematician; History of mathematics in Islamic culture; Mathematics in the Middle-East; Islamic mathematicians; Arabian mathematics; Arab mathematics; Arabic mathematics; Medieval Islamic Mathematics; Medieval Islamic mathematics; Islamic mathematics; Mathematics in the Islamic Golden Age; Mathematics in the Golden Age of Islam; Mathematics in the Caliphates; Saracenic mathematics; Islamic maths; Islamic geometry; Arabic mathematic; Algebra in medieval Islam; Irrational numbers in medieval Islam; Mathematics in medieval Islam
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta). Important progress was made, such as full development of the decimal place-value system to include decimal fractions, the first systematised study of algebra, and advances in geometry and trigonometry.
Wikipedia
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional cases.
