A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
The observable universe is a spherical region of the universe consisting of all matter that can be observed from Earth; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Assuming the universe is isotropic, the distance to the edge of the observable universe is the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.
The word observable in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the physical limit created by the speed of light itself. No signal can travel faster than light, hence there is a maximum distance, called the particle horizon, beyond which nothing can be detected, as the signals could not have reached the observer yet.
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.
In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle. A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle.
Three points in the plane that do not all fall on a straight line are concyclic, so every triangle is a cyclic polygon, with a well-defined circumcircle. However, four or more points in the plane are not necessarily concyclic. After triangles, the special case of cyclic quadrilaterals has been most extensively studied.
Alice Springs (Eastern Arrernte: Mparntwe, [ᵐbaⁿɖʷə]) is a town in the Northern Territory, Australia; it is the third-largest settlement after Darwin and Palmerston. The name Alice Springs was given by surveyor William Whitfield Mills after Alice, Lady Todd (née Alice Gillam Bell), wife of the telegraph pioneer Sir Charles Todd. Known colloquially as The Alice or simply Alice, the town is situated roughly in Australia's geographic centre. It is nearly equidistant from Adelaide and Darwin.
The area is also known locally as Mparntwe to its original inhabitants, the Arrernte, who have lived in the Central Australian desert in and around what is now Alice Springs for tens of thousands of years.
Corning is a city in Steuben County, New York, United States, on the Chemung River. The population was 10,551 at the 2020 census. It is named for Erastus Corning, an Albany financier and railroad executive who was an investor in the company that developed the community. The city is best known as the headquarters of Fortune 500 company Corning Incorporated, formerly Corning Glass Works, a manufacturer of glass and ceramic products for industrial, scientific and technical uses. Corning is roughly equidistant from New York City and Toronto, being about 220 miles (350 km) from both.