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Cardioid - Wikipedia
In geometry, a cardioid (from Greek καρδιά (kardiá) 'heart') is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse curve of the parabola with the … See more
Let $${\displaystyle a}$$ be the common radius of the two generating circles with midpoints $${\displaystyle (-a,0),(a,0)}$$, See more
Choosing other positions of the cardioid within the coordinate system results in different equations. The picture shows the 4 most common positions of a cardioid and their polar equations. See more
Chords through the cusp
C1 Chords through the cusp of the cardioid have the same length $${\displaystyle 4a}$$. C2 The midpoints of the chords through the cusp lie … See moreAn orthogonal trajectory of a pencil of curves is a curve which intersects any curve of the pencil orthogonally. For cardioids the following is true:
(The second pencil can be considered as reflections at the y-axis of the first one. See diagram.) See moreIn complex analysis, the image of any circle through the origin under the map $${\displaystyle z\to z^{2}}$$ is a cardioid. One application of this result is that the boundary of the … See more
Wikipedia text under CC-BY-SA license Space cardioid - Wikipedia
The space cardioid is a 3-dimensional curve derived from the cardioid. It has a parametric representation using trigonometric functions, as follows: [1]
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Cardioidă - Wikipedia
În geometrie, cardioida este o epicicloidă cu o cuspidă. Cardioida este o curbă plană descrisă de un punct de pe un cerc în timp ce acesta se rostogolește, fără alunecare, pe un alt cerc fix, exterior și de aceeași rază.
Cardioida este, de asemenea, și un caz particular al melcului lui Pascal: este un melc cu o cuspidă. Cuspida este formată atunci când raportul dintre a și b din ecuație este echiunitar.Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 2 mins
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Plotting algorithms for the Mandelbrot set - Wikipedia
In both the unoptimized and optimized escape time algorithms, the x and y locations of each point are used as starting values in a repeating, or iterating calculation (described in detail below). …
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CARDIOID Definition & Meaning - Merriam-Webster
The meaning of CARDIOID is a heart-shaped curve that is traced by a point on the circumference of a circle rolling completely around an equal fixed circle and has an equation in one of the forms ρ = a (1 ± cos θ) or ρ = a (1 ± sin θ) in …
Cardioid - Encyclopedia of Mathematics
Mar 26, 2023 · A plane algebraic curve of order four which is described by a point $M$ of a circle of radius $r$ rolling on a circle with the same radius $r$; an epicycloid with modulus $m=1$. The equation of the cardioid in polar …
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cardioid - Wiktionary, the free dictionary
Jan 8, 2025 · cardioid (plural cardioids) An epicycloid with exactly one cusp; the plane curve with polar equation = + - approximately heart-shaped
Cardioid - GeeksforGeeks
May 27, 2024 · Cardioid is the part of the epicycloid when the two circles have the same radius. Mathematically, a cardioid can be defined as the locus of points traced by a fixed point on the …
Category : Cardioids - Wikimedia
Feb 29, 2024 · Vintage Stromberg-Carlson Model MC-41 Cardioid Microphone, Made In USA, Uni-Directional Dynamic Type (19301544142).jpg 1,456 × 3,335; 1.58 MB Điện tâm đồ.gif 200 …
Cardioid - MacTutor History of Mathematics
The cardioid, a name first used by de Castillon in a paper in the Philosophical Transactions of the Royal Societyin 1741, is a curve that is the locus of a point on the circumference of circle rolling round the circumference of a circle of equal …
cardioid is a curve that can be produced as a locus — by tracing the path of a chosen point of a circle which rolls without slipping around another circle which is fixed but which has the same …
Cardioid -- from Wolfram MathWorld
Mar 5, 2025 · The cardioid is a degenerate case of the limaçon. It is also a 1-cusped epicycloid (with ) and is the catacaustic formed by rays originating at a point on the circumference of a …
Cardioid - Wikiwand
In geometry, a cardioid (from Greek καρδιά (kardiá) 'heart') is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be …
SilverCardioid | silvercardioid.github.io
A cardioid (car-dee-oid) is a mathematical curve resembling a rounded heart. It is the shape traced by a point on a circle rolling around another circle of the same size. It appears in …
Paths, Cardioid - mathreference.com
The cardioid is a well known graph in polar coordinates. As its name suggests, the shape resembles a heart. However, the heart is lying on its side, rotated clockwise from its traditional …
Cardioid - Academic Dictionaries and Encyclopedias
In geometry, the cardioid is an epicycloid with one cusp. Construction * epicycloid produced as the path (or locus ) of a point on the circumference of a circle as that circle rolls around another …
Cardioid - (Honors Pre-Calculus) - Vocab, Definition ... - Fiveable
A cardioid is a specific type of polar curve that resembles a heart shape. It is defined as the locus of points traced by a point on the circumference of a circle as the circle rolls along the inside of …
Cardioid (Definition, Equations and Examples) - BYJU'S
A cardioid is a shape, defined in two dimensions, that looks like the shape of a heart. The cardioid is formed by following the path of a point on a rolling circle over another fixed circle of the …
Cardioid - Scientific Lib
A cardioid (from the Greek καρδία "heart") is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It is therefore a type of limaçon …
Cardioids - (Calculus IV) - Vocab, Definition, Explanations - Fiveable
Cardioids are heart-shaped curves that can be represented as a specific type of polar graph. They are created by tracing the path of a point on the perimeter of a circle that rolls around another …
Cardioid – Meaning, Equation, Graph and Solved Examples
The cardioid is a plane figure obtained as a path followed by a circle of certain radius over the circumference of a fixed circle of the same radius. A cardioid can be represented in both polar …
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