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Special triangle in geometry
The Calabi triangle is a special triangle found by Eugenio Calabi. It is the unique triangle that has 3 different placements for the largest square that
Calabi_triangle
Shape with three sides
relation is the Calabi triangle in which the vertices of every three squares are tangent to all obtuse triangle's sides. Every acute triangle has three inscribed
Triangle
Square whose vertices lie on a triangle
between them, must lie on one of the sides of the triangle. For instance, for the Calabi triangle depicted, the square with horizontal and vertical sides
Inscribed square in a triangle
Inscribed_square_in_a_triangle
Triangle with at least two sides congruent
isosceles right triangle, several other specific shapes of isosceles triangles have been studied. These include the Calabi triangle (a triangle with three
Isosceles_triangle
Triangles without a right angle
acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle
Acute_and_obtuse_triangles
Italian-born American mathematician (1923–2023)
Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University
Eugenio_Calabi
Shape with four equal sides and angles
Squares can be inscribed in any smooth or convex curve, such as a circle or triangle, but it remains unsolved whether a square can be inscribed in every simple
Square
Generalized manifold
compactified space must be a 6-dimensional Calabi–Yau manifold. There are a large number of possible Calabi–Yau manifolds (tens of thousands), hence the
Orbifold
Theory of subatomic structure
physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to
String_theory
Study of complex manifolds and several complex variables
to be proven with great success, including Shing-Tung Yau's proof of the Calabi conjecture, the Hitchin–Kobayashi correspondence, the nonabelian Hodge correspondence
Complex_geometry
Category in mathematics
homological mirror symmetry conjecture predicts that the derived category of a Calabi–Yau manifold is equivalent to the Fukaya category of its "mirror" symplectic
Triangulated_category
Conjecture in symplectic geometry
that mirror to a symplectic manifold (which is a Calabi–Yau manifold) there should be another Calabi–Yau manifold for which the symplectic structure is
Thomas–Yau_conjecture
Branch of mathematics
examples of spaces studied in complex geometry include Riemann surfaces, and Calabi–Yau manifolds, and these spaces find uses in string theory. In particular
Geometry
Framework of superstring theory
six-dimensional Calabi–Yau manifold. This is a special kind of geometric object named after mathematicians Eugenio Calabi and Shing-Tung Yau. Calabi–Yau manifolds
M-theory
Stability conditions for triangulated cateogires
triangulated category is the derived category of coherent sheaves on a Calabi–Yau manifold, and this situation has fundamental links to string theory
Bridgeland stability condition
Bridgeland_stability_condition
Class of algebraic theorems
_{n}(\mathbb {R} )} . Shortly afterwards a similar statement was proven by Eugenio Calabi in the setting of fundamental groups of compact hyperbolic manifolds. Finally
Local_rigidity
label), bladder cancer. Eugenio Calabi, 100, Italian-born American mathematician (Calabi conjecture, Calabi–Yau manifold, Calabi flow). Bob Dahl, 54, American
Deaths_in_September_2023
American physicist
theory-based approaches inspired by particle physics. In 1985 he co-discovered Calabi–Yau manifold compactifications, showing that a superstring theory could
Andrew_Strominger
Algebraic structure
Ruddat, Helge; Thompson, Alan (2015). "An Introduction to Hodge Structures". Calabi-Yau Varieties: Arithmetic, Geometry and Physics. Fields Institute Monographs
Mixed_Hodge_structure
polyhedron models Jean-Louis Koszul (1921–2018) Isaak Yaglom (1921–1988) Eugenio Calabi (1923–2023) Benoit Mandelbrot (1924–2010) – fractal geometry Katsumi Nomizu
List_of_geometers
Property of a mathematical space
superstring theory requires six compact dimensions (6D hyperspace) forming a Calabi–Yau manifold. Thus Kaluza-Klein theory may be considered either as an incomplete
Dimension
Symplectic topology tool
homology of Lagrangians in a Calabi–Yau manifold X {\displaystyle X} and the Ext groups of coherent sheaves on the mirror Calabi–Yau manifold. In this situation
Floer_homology
Theorem in differential geometry
the fundamental Laplacian comparison theorem proved earlier by Eugenio Calabi, these functions are both superharmonic under the Ricci curvature assumption
Splitting_theorem
Principle in theoretical physics
Lectures on the Infrared Structure of Gravity and Gauge Theory, the infrared triangle, proposed to constrain theories of quantum gravity, could be used to show
Holographic_principle
Mathematics study in geometry
{\displaystyle X} is Calabi–Yau, since ω X ≅ O X {\displaystyle \omega _{X}\cong {\mathcal {O}}_{X}} , or is the product of a variety which is Calabi–Yau. Abelian
Derived noncommutative algebraic geometry
Derived_noncommutative_algebraic_geometry
Mathematical set with some added structure
space Base space Bergman space Berkovich space Besov space Borel space Calabi-Yau space Cantor space Cauchy space Cellular space Chu space Closure space
Space_(mathematics)
Mathematics timeline
smooth projective Calabi–Yau variety of dimension d then D b ( Coh ( X ) ) {\displaystyle D^{b}(\operatorname {Coh} (X))} is a unital Calabi–Yau A∞-category
Timeline_of_manifolds
Algebraic curve in mathematics
p. 160 Harris, M.; Shepherd-Barron, N.; Taylor, R. (2010). "A family of Calabi–Yau varieties and potential automorphy". Annals of Mathematics. 171 (2):
Elliptic_curve
History of maths
smooth projective Calabi—Yau variety of dimension d then Db(Coh(X)) is a unital Calabi–Yau A∞-category of Calabi–Yau dimension d. A Calabi–Yau category with
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Duality between theories of gravity on anti-de Sitter space and conformal field theories
tessellation of a disk by triangles and squares. One can define the distance between points of this disk in such a way that all the triangles and squares are the
AdS/CFT_correspondence
Mathematical group of the homotopy classes of loops in a topological space
remark in a paper by André Weil; various other authors such as Lorenzo Calabi, Wu Wen-tsün, and Nodar Berikashvili have also published proofs. In the
Fundamental_group
Soviet and Russian mathematician
Monge-Ampere equations. This was the main step in the proof of the existence of Calabi-Yau manifolds, which play an important role in theoretical physics. A Monge-Ampère
Aleksei_Pogorelov
Academic department at Princeton University
professor of mathematics, Morningside Gold Medal of Mathematics (1998) Eugenio Calabi (Ph.D., 1950) – professor emeritus, University of Pennsylvania; Leroy P
Department of Mathematics (Princeton University)
Department_of_Mathematics_(Princeton_University)
Asymmetry of classical and quantum action
Wa, Wb and one hypercharge B at the vertices of the triangle diagram, cancellation of the triangle requires ∑ a l l d o u b l e t s T r T a T b Y ∝
Anomaly_(physics)
Generalization of electrodynamics
theorems and memory effects. This connection is often called the infrared triangle. Interest in studying asymptotic symmetries in p-form theories is primarily
P-form_electrodynamics
from the original on May 5, 2010. Retrieved October 20, 2011. "Eugenio Calabi". Mathematics Genealogy Project. Retrieved October 24, 2011. "David Card"
List of Princeton University people
List_of_Princeton_University_people
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