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By analogy with the square root of x, one can define the (positive) triangular root of x as the number n such that T n = x: [17] = + which follows immediately from the quadratic formula . So an integer x is triangular if and only if 8 x + 1 is a square.
As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon , all the diagonals are inside the polygon, but for re-entrant polygons , some diagonals are outside of the polygon.
In noncommutative geometry and related branches of mathematics and mathematical physics, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The definition typically involves a Hilbert space , an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures.
A plane conic passing through the circular points at infinity. For real projective geometry this is much the same as a circle in the usual sense, but for complex projective geometry it is different: for example, circles have underlying topological spaces given by a 2-sphere rather than a 1-sphere. circuit A component of a real algebraic curve.
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in R n , {\displaystyle \mathbb {R} ^{n},} and the study of these lattices provides fundamental information on algebraic numbers. [ 1 ]