Hypocycloid, the Glossary

Table of Contents

1. 43 relations: Albrecht Dürer, Arc length, Astroid, Astronomy in the medieval Islamic world, Brachistochrone curve, Circle, Crank (mechanism), Cusp (singularity), Cyclogon, Cycloid, Deltoid curve, Differentiable function, Epicycloid, Epitrochoid, Evolute, Flag of Portland, Oregon, Geometry, Gregg Easterbrook, High-definition television, Huachipato FC, Hypotrochoid, Involute, Irrational number, List of periodic functions, Mathematics in the medieval Islamic world, Murray's Hypocycloidal Engine, Nasir al-Din al-Tusi, Orthoptic (geometry), Parametric equation, Pedal curve, Persians, Pittsburgh Steelers, Plane curve, Printing press, Rational number, Rose (mathematics), Roulette (curve), Special unitary group, Spirograph, Steelmark, Subgroup, The Price Is Right, Tusi couple.

2. Roulettes (curve)

Albrecht Dürer

Albrecht Dürer (21 May 1471 – 6 April 1528),Müller, Peter O. (1993) Substantiv-Derivation in Den Schriften Albrecht Dürers, Walter de Gruyter.

See Hypocycloid and Albrecht Dürer

Arc length

Arc length is the distance between two points along a section of a curve.

See Hypocycloid and Arc length

Astroid

In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Hypocycloid and astroid are roulettes (curve).

See Hypocycloid and Astroid

Astronomy in the medieval Islamic world

Medieval Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries), and mostly written in the Arabic language.

See Hypocycloid and Astronomy in the medieval Islamic world

Brachistochrone curve

In physics and mathematics, a brachistochrone curve, or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of a uniform gravitational field to a given end point in the shortest time.

See Hypocycloid and Brachistochrone curve

Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

See Hypocycloid and Circle

Crank (mechanism)

A crank is an arm attached at a right angle to a rotating shaft by which circular motion is imparted to or received from the shaft.

See Hypocycloid and Crank (mechanism)

Cusp (singularity)

In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction.

See Hypocycloid and Cusp (singularity)

Cyclogon

In geometry, a cyclogon is the curve traced by a vertex of a regular polygon that rolls without slipping along a straight line. Hypocycloid and cyclogon are roulettes (curve).

See Hypocycloid and Cyclogon

Cycloid

In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. Hypocycloid and cycloid are roulettes (curve).

See Hypocycloid and Cycloid

Deltoid curve

In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. Hypocycloid and deltoid curve are roulettes (curve).

See Hypocycloid and Deltoid curve

Differentiable function

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

See Hypocycloid and Differentiable function

Epicycloid

In geometry, an epicycloid (also called hypercycloid) is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. Hypocycloid and epicycloid are roulettes (curve).

See Hypocycloid and Epicycloid

Epitrochoid

In geometry, an epitrochoid is a roulette traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius, where the point is at a distance from the center of the exterior circle. Hypocycloid and epitrochoid are roulettes (curve).

See Hypocycloid and Epitrochoid

Evolute

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature.

See Hypocycloid and Evolute

Flag of Portland, Oregon

The city flag of Portland, Oregon, consists of a green field on which is placed a white four-pointed star (a truncated hypocycloid) from which radiate blue stripes, each bordered by L-shaped yellow elements (''esquarres'').

See Hypocycloid and Flag of Portland, Oregon

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Hypocycloid and Geometry

Gregg Easterbrook

Gregg Edmund Easterbrook (born March 3, 1953) is an American writer and a contributing editor of both The New Republic and The Atlantic Monthly.

See Hypocycloid and Gregg Easterbrook

High-definition television

High-definition television (HDTV) describes a television or video system which provides a substantially higher image resolution than the previous generation of technologies.

See Hypocycloid and High-definition television

Huachipato FC

Huachipato FC is a Chilean football club based in Talcahuano that currently plays in the Chilean Primera División.

See Hypocycloid and Huachipato FC

Hypotrochoid

In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius rolling around the inside of a fixed circle of radius, where the point is a distance from the center of the interior circle. Hypocycloid and hypotrochoid are roulettes (curve).

See Hypocycloid and Hypotrochoid

Involute

In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. Hypocycloid and involute are roulettes (curve).

See Hypocycloid and Involute

Irrational number

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.

See Hypocycloid and Irrational number

List of periodic functions

This is a list of some well-known periodic functions.

See Hypocycloid and List of periodic functions

Mathematics in the medieval Islamic world

Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).

See Hypocycloid and Mathematics in the medieval Islamic world

Murray's Hypocycloidal Engine

Murray's Hypocycloidal Engine, now in Thinktank, Birmingham Science Museum, England, was made around 1805 and is the world's third-oldest working steam engine and the oldest working engine with a Tusi couple hypocycloidal straight line mechanism.

See Hypocycloid and Murray's Hypocycloidal Engine

Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tusi (1201 – 1274), also known as Nasir al-Din al-Tusi (نصیر الدین الطوسی; نصیر الدین طوسی) or simply as (al-)Tusi, was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

See Hypocycloid and Nasir al-Din al-Tusi

Orthoptic (geometry)

In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle.

See Hypocycloid and Orthoptic (geometry)

Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

See Hypocycloid and Parametric equation

Pedal curve

In mathematics, a pedal curve of a given curve results from the orthogonal projection of a fixed point on the tangent lines of this curve.

See Hypocycloid and Pedal curve

Persians

The Persians--> are an Iranian ethnic group who comprise over half of the population of Iran.

See Hypocycloid and Persians

Pittsburgh Steelers

The Pittsburgh Steelers are a professional American football team based in Pittsburgh.

See Hypocycloid and Pittsburgh Steelers

Plane curve

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane.

See Hypocycloid and Plane curve

Printing press

A printing press is a mechanical device for applying pressure to an inked surface resting upon a print medium (such as paper or cloth), thereby transferring the ink.

See Hypocycloid and Printing press

Rational number

In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

See Hypocycloid and Rational number

Rose (mathematics)

In mathematics, a rose or rhodonea curve is a sinusoid specified by either the cosine or sine functions with no phase angle that is plotted in polar coordinates.

See Hypocycloid and Rose (mathematics)

Roulette (curve)

In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes. Hypocycloid and roulette (curve) are roulettes (curve).

See Hypocycloid and Roulette (curve)

Special unitary group

In mathematics, the special unitary group of degree, denoted, is the Lie group of unitary matrices with determinant 1.

See Hypocycloid and Special unitary group

Spirograph

Spirograph is a geometric drawing device that produces mathematical roulette curves of the variety technically known as hypotrochoids and epitrochoids.

See Hypocycloid and Spirograph

Steelmark

The Steelmark is a logo representing steel and the steel industry owned by the American Iron and Steel Institute, and used by it to promote the product and its manufacturers.

See Hypocycloid and Steelmark

Subgroup

In group theory, a branch of mathematics, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗.

See Hypocycloid and Subgroup

The Price Is Right

The Price Is Right is an American television game show where contestants compete by guessing the prices of merchandise to win cash and prizes.

See Hypocycloid and The Price Is Right

Tusi couple

The Tusi couple (also known as Tusi's mechanism) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Hypocycloid and Tusi couple are roulettes (curve).

See Hypocycloid and Tusi couple

See also

Roulettes (curve)

• Astroid
• Cardioid
• Catenary
• Centered trochoid
• Cissoid of Diocles
• Cyclogon
• Cycloid
• Cycloid gear
• Deltoid curve
• Epicycloid
• Epitrochoid
• Hypocycloid
• Hypotrochoid
• Involute
• Limaçon
• Limaçon trisectrix
• Nephroid
• Roulette (curve)
• Trochoid
• Tusi couple

References

[1] https://en.wikipedia.org/wiki/Hypocycloid

Also known as Hypocycloidal, Hypocycloids.