A tri-oval is a shape which derives its name from the two other shapes it most resembles, a

triangle A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

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 (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or ...

. 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 The four-vertex theorem of geometry 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 fro ...

, every smooth

simple closed curve In topology, the Jordan curve theorem asserts that every ''Jordan curve'' (a plane simple closed curve) divides the plane into an " interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior ...

has at least four vertices, points where its

curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...

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 u ...

s. The use of the tri-oval shape for automobile racing was conceived by Bill France Sr. 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 state capital and most populous city of the U.S. state of Indiana and the seat of Marion County. According to the U.S. Census Bureau, the consolidated population of Indianapolis and 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.

References

{{reflist Geometric shapes

Use in racetracks

See also

References