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Exemplary triangular function. A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often this is an isosceles triangle of height 1 and base 2 in which case it is referred to as the triangular function.
The Källén function, also known as triangle function, is a polynomial function in three variables, which appears in geometry and particle physics. In the latter field it is usually denoted by the symbol λ {\displaystyle \lambda } .
Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The nth coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the nth region is n times n x n.
In the proof this is first shown only for simplicial maps and then generalized for any continuous functions via the approximation theorem. Brouwer's fixpoint theorem treats the case where f : D n → D n {\displaystyle f:\mathbb {D} ^{n}\rightarrow \mathbb {D} ^{n}} is an endomorphism of the unit-ball.
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A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. [1] It graphically depicts the ratios of the three variables as positions in an equilateral triangle .
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