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The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

Given an acute angle in a right triangle, the adjacent side is the leg of the triangle from which the angle to the hypotenuse is measured. Lengths of adjacent and opposite ...

Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of ...

A unit of angular measure in which the angle of an entire circle is 400 gradians. A right angle is therefore 100 gradians. A gradian is sometimes also called a gon or a grade.

The L^2-inner product of two real functions f and g on a measure space X with respect to the measure mu is given by <f,g>_(L^2)=int_Xfgdmu, sometimes also called the bracket ...

∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...

The angles S_1=A_1/2 and S_2=A_2/2 obtained from solving sin(x+omega)=2sinomega (1) for x=A_1,A_2, where omega is the Brocard angle. The half-angles A_1 and A_2 are given by ...

Construction of the angle pi/3=60 degrees produces a 30-60-90 triangle, which has angles theta=pi/3 and theta/2=pi/6. From the above diagram, write y=sintheta for the ...