Triangle by moving the triangle, rotating it, or reflecting it as in a mirror, any of which give a congruent triangle, or even by rescaling it to give a similar triangle: A non-planar triangle is a triangle which is not contained in a (flat) plane. Some examples of non-planar triangles in non-Euclidean geometries are spherical triangles in spherical geometry and hyperbolic triangles in hyperbolic geometry. While the measures of the internal angles in planar triangles always sum to 180°, a hyperbolic triangle has measures of angles that sum to less than 180°, and a spherical triangle has measures of angles that
Leibniz harmonic triangle formula_4 Whereformula_5is a binomial coefficient Whereas each entry in Pascal's triangle is the sum of the two entries in the above row, each entry in the Leibniz triangle is the sum of the two entries in the row "below" it. For example, in the 5th row, the entry (1/30) is the sum of the two (1/60)s in the 6th row. Just as Pascal's triangle can be computed by using binomial coefficients, so can Leibniz's: formula_6. Furthermore, the entries of this triangle can be computed from Pascal's: "The terms in each row are the initial term divided by the corresponding Pascal