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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. While it is not generally used in formal writing, it is used in mathematics and shorthand.
Symbol Name Symbol(s) Meaning Example of Use Dele: Delete: Pilcrow (Unicode U+00B6) ¶ Begin new paragraph: Pilcrow (Unicode U+00B6) ¶ no: Remove paragraph break: Caret [a] (Unicode U+2038, 2041, 2380) ‸ or ⁁ or ⎀ Insert # Insert space: Close up (Unicode U+2050) ⁐ Tie words together, eliminating a space: I was reading the news⁐paper ...
The triple bar or tribar, ≡, is a symbol with multiple, context-dependent meanings indicating equivalence of two different things. Its main uses are in mathematics and logic. It has the appearance of an equals sign = with a third line.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.
In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three points called angles or vertices. Just as in the Euclidean case, three points of a hyperbolic space of an arbitrary dimension always lie on the same plane. Hence planar hyperbolic triangles also ...
A particularly elegant proof is due to François-Joseph Servois (1804) and independently Carl Friedrich Gauss (1810): Draw a line parallel to each side of the triangle through the opposite point, and form a new triangle from the intersections of these three lines. Then the original triangle is the medial triangle of the new triangle, and the ...
Whereas Roberts's theorem concerns the fewest possible triangles made by a given number of lines, the related Kobon triangle problem concerns the largest number possible. [3] The two problems differ already for n = 5 {\displaystyle n=5} , where Roberts's theorem guarantees that three triangles will exist, but the solution to the Kobon triangle ...