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What (who) is G2 (mathematics) - definition
SIMPLE LIE GROUP; THE AUTOMORPHISM GROUP OF THE OCTONIONS
G2 (math); G2 (Mathematics); G2 (group); G₂
G2 (mathematics)
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak{g}_2, as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups.
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
G2 (mathematics)
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14.
The compact form of G2 can be described as the automorphism group of the octonion algebra or, equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation (a spin representation).
