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
Circle packing in an equilateral triangle Circle packing in an equilateral triangle Circle packing in an equilateral triangle is a packing problem in discrete mathematics where the objective is to pack "n" unit circles into the smallest possible equilateral triangle. Optimal solutions are known for "n" < 13 and for any triangular number of circles, and conjectures are available for "n" < 28. A conjecture of Paul Erdős and Norman Oler states that, if is a triangular number, then the optimal packings of and of circles have the same side length: that is, according to the conjecture, an optimal packing for circles can be found by