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The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
The altitude from A (dashed line segment) intersects the extended base at D (a point outside the triangle). In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite the apex.
The vertices of triangles are associated not only with spatial position but also with other values used to render the object correctly. Most attributes of a vertex represent vectors in the space to be rendered.
In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length and two angles of equal measure. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Plots of logarithm functions, with three commonly used bases. The special points log b b = 1 are indicated by dotted lines, and all curves intersect in log b 1 = 0. In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.
Within the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself. This implies that a singleton is necessarily distinct from the element it contains, [1] thus 1 and {} are not the same thing, and the empty set is distinct from the set containing only the empty set.