Therefore sign specialized keyboards and fonts, and to prevent compatibility issues, it's often substituted by a colon followed by a period (":.") even if it's considered more elegant to use the original therefore character in printing. Therefore sign In logical argument and mathematical proof, the therefore sign (∴) is generally used before a logical consequence, such as the conclusion of a syllogism. The symbol consists of three dots placed in an upright triangle and is read "therefore". It is encoded at . For common use in Microsoft Office hold the ALT key and type "8756". While it is not generally used in
Equilateral triangle the location of "P". Pompeiu's theorem states that, if "P" is an arbitrary point in an equilateral triangle "ABC", then there exists a triangle with sides of lengths "PA", "PB", and "PC". That is, "PA", "PB", and "PC" satisfy the triangle inequality that any two of them sum to at least as great as the third. By Euler's inequality, the equilateral triangle has the smallest ratio "R"/"r" of the circumradius to the inradius of any triangle: specifically, "R"/"r" = 2. The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest