Geometry Camp

In mathematics, a distance or metric is a function that defines a distance between each pair of elements of a set. A set is a collection of elements, and the distance between two elements a and b of this set is defined as the minimum number of steps needed to get from a to b, where the steps are taken along the edges connecting a and b. In other words, the distance is the minimum number of edges that have to be passed from a to b. The distance may be thought of as the length of the smallest path connecting the two points.

In mathematics, a distance matrix is a matrix whose rows and columns are the distances between pairs of the set of points from which the matrix is constructed. The entries of the matrix are non-negative and sum to the total distance between the points.

In mathematics, a line is a straight line segment with zero curvature, meaning that it is a line in the Euclidean plane with no inflection points. The concept of a line is one of the most fundamental concepts in geometry, building a bridge between Euclidean geometry and algebra. In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For example, in analytic geometry a line may be defined as a set of points satisfying a linear equation, while in synthetic geometry it is described as a set of points satisfying a geometric theorem.

In mathematics, the equations of a line are parametric equations, usually written in the form (x?x_1)/cos? ? = (y?y _1)/sin? =r, where r is the parameter which is distance between the point (x,y) and (x_1,y_1).

In mathematics, the midpoint formula is a formula for the coordinates of the midpoint of a line segment between two points with Cartesian coordinates (x1, y1) and (x2, y2).

In geometry, the midpoint formula is used to find the coordinates of the midpoint of a line segment between two points in the Euclidean plane.

A line is a one-dimensional linear object with no thickness, length, width, or breadth. A line is either straight or curved.

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

In mathematics, partitioning a line segment is a way of dividing a line segment into two, three, or more line segments of equal length. The partitions of a line segment are the collection of all the ways of dividing it. For example, one can partition a line segment into two equal pieces by dividing it at its midpoint or by dividing it into three equal pieces by dividing it at its midpoint twice.

In mathematics, the perpendicular bisector of a segment is a line that passes through the midpoint of the segment and is perpendicular to it. The perpendicular bisector of a ray is a line that passes through the midpoint of the ray and is perpendicular to it.

In geometry, a perpendicular line is a line perpendicular to another line. The word "perpendicular" comes from the Latin word "perpendiculum", meaning "a rod to hang from". The perpendicular is the line that is perpendicular to the plane of the other line. The definition of perpendicular lines is based on two equivalent definitions: A line is perpendicular to another line if the two lines intersect and no point on the second line lies on the first line. A line is perpendicular to another line if the two lines are not parallel and a point on the second line lies on the first line. The first definition follows from the second, since the angle between two lines is 90 degrees.

In mathematics, a partition of a set "S" is a collection of non-empty subsets of "S" such that every element is contained in exactly one of the subsets. The partition (or disjoint-set data structure) problem is the problem of finding a partition of a given set "S" into a minimum number of non-empty subsets. The problem was first formulated in 1936 by Frank Rubin and is also known as the "Rubin partition problem".

Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. Parallel planes are planes in the same three-dimensional space that never meet.