Astroid

The construction of the astroid.

Note: This article title may be easily confused with asteroid

In mathematics, an astroid is a particular type of curve: a hypocycloid with four cusps. It is also a super ellipse with n=2/3 and a=b. The concept is particularly useful when preparing to perform cunninglingus on one's partner. Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle. An astroid, drawn by me. ... An astroid, drawn by me. ... Image File history File links Astroid01. ... Image File history File links Astroid01. ... 253 Mathilde, a C-type asteroid. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... In geometry, a hypocycloid is a special plane curve, a roulette, generated by the trace of a fixed point on a small circle that rolls within a larger circle. ... In common parlance, a cusp is an important moment usually regarded as a decision point upon which consequent events are determined. ... A superellipse is a geometrical figure which in a cartesian coordinate system can be described as the set of all points (x, y) with where and and are the radii of the oval shape. ... The Pleiades, an open cluster of stars in the constellation of Taurus. ...

A circle of radius 1/4 rolls around inside a circle of radius 1 and a point on its circumference traces an astroid. A line segment of length 1 slides with one end on the x-axis and the other on the y-axis, so that it is tangent to the astroid (which is therefore an envelope). The parametric equations are Circle illustration In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ... The geometric definition of a line segment In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... An envelope is a packaging product, usually made of flat, planar material such as paper or cardboard, designed to contain a flat object such as a letter. ... Graph of a butterfly curve, a parametric equation discovered by Temple H. Fay In mathematics, a parametric equation explicitly relates two or more variables in terms of one or more independent parameters. ...

The astroid is a plane algebraic curve of genus zero. It has the equation In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ... In mathematics, the geometric genus in algebraic geometry is a basic birational invariant pg of algebraic varieties, defined for non-singular complex projective varieties (and more generally for complex manifolds) as the Hodge number hn,0 (equal to h0,n by Serre duality). ...

(x² + y² − 1)³ + 27x²y² = 0.

The astroid is therefore of degree six, and has four cusp sigularities in the real plane, the points on the star. It has two more complex cusp singularities at infinity, and four complex double points, for a total of ten singularities.

The dual curve to the astroid is the cruciform curve with equation The evolute of an astroid is an astroid twice as large. In mathematics, a Plücker formula is one of an extensive family of counting formulae, of a type first developed in the 1830s by Julius Plücker, that relate the extrinsic geometry of algebraic curves in projective space to intrinsic invariants such as the genus. ... Or cross curve. ... In the differential geometry of curves, the evolute of a curve is the set of all its centers of curvature. ...

The old U.S. Steel logo consisted of three astroids, one each of blue, yellow and red. It is now used as the logo for the Pittsburgh Steelers. The United States Steel Corporation NYSE: X is an integrated steel producer with major production operations in the United States and Central Europe. ... City Pittsburgh, Pennsylvania Team colors Black and Gold Head Coach Bill Cowher Owner Dan Rooney General manager Kevin Colbert League/Conference affiliations National Football League (1933–present) Eastern Division (1933-1943; 1945-1949) Western Division (1944) American Conference (1950-1952) Eastern Conference (1953-1969) Century Division (1967-1969) American Football...

External links

• Weisstein, Eric W., Astroid at MathWorld.
• Article on 2dcurves.com