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A tri-oval is a shape which derives its name from the two other shapes it most resembles, a
This term is most often used to describe the shape of many automobile
triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...
and an oval
An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition, which may inc ...
. Rather than meeting at sharp, definable angles as the sides of a triangle do, in a tri-oval these angles are instead rounded into smooth curves.
While an oval has four turns, a tri-oval has six. More formally, according to the four-vertex theorem
In geometry, the four-vertex theorem states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives ...
, every smooth simple closed curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...
has at least four vertices, points where its curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or su ...
reaches a local minimum or maximum. In a tri-oval, there are six such points, alternating between three minima and three maxima.
Use in racetracks
This term is most often used to describe the shape of many automobile racetrack
A race track (racetrack, racing track or racing circuit) is a facility built for racing of vehicles, athletes, or animals (e.g. horse racing or greyhound racing). A race track also may feature grandstands or concourses. Race tracks are also us ...
s.
The use of the tri-oval shape for automobile racing was conceived by Bill France Sr.
William Henry Getty France (September 26, 1909 – June 7, 1992) was an American businessman and racing driver. He was also known as Bill France Sr. or Big Bill. He is best known for founding and managing NASCAR, a sanctioning body of US-based s ...
during the planning for Daytona. The triangular layout allowed fans in the grandstands an angular perspective of the cars coming towards and moving away from their vantage point. Traditional ovals (such as Indianapolis
Indianapolis ( ), colloquially known as Indy, is the List of capitals in the United States, capital and List of municipalities in Indiana, most populous city of the U.S. state of Indiana and the county seat of Marion County, Indiana, Marion ...
) offered only limited linear views of the course, and required fans to look back and forth much like a tennis match. The tri-oval shape prevents fans from having to "lean" to see oncoming cars, and creates more forward sight lines.
In other racing vernacular, the term "tri-oval" is also used to specifically describe the part of the track which represents the top triangular point of the course, which is used as the main stretch, the pit straight and usually the start–finish line. It is recognizable in most tracks by a manicured grass area.
The modern tri-ovals were often called ''cookie cutters'' because of their (nearly) identical shape and identical kind of races.
See also
*Bean curve
In algebraic geometry, a quartic plane curve is a plane algebraic curve of the fourth degree of a polynomial, degree. It can be defined by a bivariate quartic equation:
:Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0 ...
, a quartic curve
*n-ellipse
In geometry, the -ellipse is a generalization of the ellipse allowing more than two foci. -ellipses go by numerous other names, including multifocal ellipse, polyellipse, egglipse, -ellipse, and Tschirnhaus'sche Eikurve (after Ehrenfried Walt ...
, a family of curves that includes some tri-ovals
*Reuleaux triangle
A Reuleaux triangle is a circular triangle, curved triangle with curve of constant width, constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circle, circular dis ...
, also called a spherical triangle
References
{{reflist Geometric shapes