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2. Foundations of geometry - Wikipedia

   en.wikipedia.org/wiki/Foundations_of_geometry

   Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.

3. K-set (geometry) - Wikipedia

   en.wikipedia.org/wiki/K-set_(geometry)

   A set of six points (red), its six 2-sets (the sets of points contained in the blue ovals), and lines separating each -set from the remaining points (dashed black). In discrete geometry , a k {\displaystyle k} -set of a finite point set S {\displaystyle S} in the Euclidean plane is a subset of k {\displaystyle k} elements of S {\displaystyle S ...

4. Set (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Set_(mathematics)

   A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...

5. Locus (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Locus_(mathematics)

   Each curve in this example is a locus defined as the conchoid of the point P and the line l.In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

6. Convex set - Wikipedia

   en.wikipedia.org/wiki/Convex_set

   Equivalently, a convex set or a convex region is a set that intersects every line in a line segment, single point, or the empty set. [1] [2] For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set in the plane is always a convex curve.

7. Straightedge and compass construction - Wikipedia

   en.wikipedia.org/wiki/Straightedge_and_compass...

   The same set of points can often be constructed using a smaller set of tools. For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x 2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction.