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A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

A chart made by plotting the numeric values of a set of quantities as a set of adjacent circular wedges with arc lengths proportional to the total amount. All wedges taken ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

The Stammler circle is the circumcircle of the Stammler triangle. Unexpectedly, it has center at the circumcenter O (X_3) of the reference triangle and radius 2R (Ehrmann and ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

Let each of f(a,b,c) and g(a,b,c) be a triangle center function or the zero function, and let one of the following three conditions hold. 1. The degree of homogeneity of g ...

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...