A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q). Dihedra have also been called bihedra, flat polyhedra, or doubly covered polygons. As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering the sphere, each face being a hemisphere, and vertices on a great circle. It is regular if the vertices are equally spaced. The dual of an n-gonal dihedron is an n-gonal hosohedron, where n digon faces share two vertices. (Wikipedia).
What is the difference between convex and concave
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
The remarkable Dihedron algebra | Famous Math Problems 21b | N J Wildberger
This is the second video on this Famous Math Problem: How to construct the (true) complex numbers? What we really want to do is proceed completely precisely and algebraically, but with as much generality as possible. For that, the Dihedron algebra D is the key ingredient. This is a sister
From playlist Famous Math Problems
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
The geometry of the Dihedrons (and Quaternions) | Famous Math Problems 21c | N J Wildberger
The Dihedrons are a sister algebra to the Quaternions. They were first explicitly introduced and named by James Cockle in 1849 -- as split-quaternions. But because of the important connections with the dihedral group D_4, we would like to introduce the name "Dihedrons" --- as this indicate
From playlist Famous Math Problems
The Square Lattice via group D4 and its hypergroups | Diffusion Symmetry 5 | N J Wildberger
Hypergroups are remarkable probabilistic/ algebraic objects that have a close connection to groups, but that allow a transformation of non-commutative problems into the commutative setting. This gives powerful new tools for harmonic analysis in situations ruled by symmetry. Bravais latti
From playlist Diffusion Symmetry: A bridge between mathematics and physics
What is the difference between concave and convex polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
The true algebra of complex numbers - via Dihedrons! | Famous Math Problems 21d | N J Wildberger
We summarize how the larger framework of the Dihedron algebra--- the 2 x 2 matrices over a general field, with a very distinguished * operation of conjugation / adjugate gives rise to a powerful approach to complex numbers. This general approach also yields the red and green versions of th
From playlist Famous Math Problems
Written and performed by TRM intern Siddiq Islam. Siddiq is a second year maths student @oxforduniversity. FULL LYRICS BELOW. Iβm in a love triangle I wish polygons existed that only had two sides Itβs not viable Between two points in Euclidean space you can only draw one line Iβm in a
From playlist Special Events and Livestreams
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are four types of polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Doris Schattschneider - Two Conway Geometric Gems - CoM Oct 2021
John Conway enjoyed discovering unusual properties of triangles and also enjoyed discovering properties of tilings. Two of his discoveries bear his name: The Conway Circle, and The Conway Criterion. Iβll talk about these two gems; one led to a new tiling app. Doris Schattschneider, profes
From playlist Celebration of Mind 2021
The k-Poly Algebra and truncations | Algebraic Calculus Two | Wild Egg Maths
We introduce finite algebraic approximations to the algebra of polynumbers called k-polys, where k is a natural number. The key notion here is that of an algebra: which is a linear or vector space with an additional (associative) multiplication that distributes with the linear structure o
From playlist Algebraic Calculus Two
The chromatic algebra of 2x2 matrices II | Wild Linear Algebra B 42 | NJ Wildberger
The three-fold symmetry of chromogeometry, involving one Euclidean and two relativistic geometries (blue, red and green), algebraically takes place inside the 2x2 matrices. This is a vector space with a multiplication, which becomes an algebra (associative with identity is included in our
From playlist WildLinAlg: A geometric course in Linear Algebra
Dual complex numbers and Leibniz's differentiation rules | Famous Math Problems 22b | N J Wildberger
We are aiming to explain a purely algebraic approach to infinitesimals that extends differential calculus to general fields -- even to finite fields. The dual complex numbers are another commutative subalgebra of the algebra of Dihedrons. They were introduced by William Clifford in 1873.
From playlist Famous Math Problems
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
How to develop a proper theory of infinitesimals I | Famous Math Problems 22a | N J Wildberger
Infinitesimals have been contentious ingredients in quadrature and calculus for thousands of years. Our definition of the term starts with the Wikipedia entry, modified a bit to reduce the dependence on "real numbers", which is actually quite unnecessary--- but as a logical definition it i
From playlist Famous Math Problems