Ellipse vs. Helix — What's the Difference?
By Maham Liaqat & Fiza Rafique — Updated on April 27, 2024
An ellipse is a flat, closed curve with two focal points, characterized by its oval shape, while a helix is a three-dimensional spiral extending in space.
Difference Between Ellipse and Helix
Table of Contents
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Key Differences
An ellipse is a planar section of a cone that results when the cutting plane is parallel to the axis of the cone, producing a smooth, closed curve. In contrast, a helix arises as a three-dimensional curve, twisting around a cylindrical or conical surface, such as in a spiral staircase.
.Ellipses are defined mathematically by two foci, where the sum of distances from any point on the ellipse to these foci is constant. This property gives the ellipse its distinctive rounded, but elongated shape. Meanwhile, a helix is characterized by its radius and pitch, where the pitch represents the height of one complete turn around the cylinder.
In terms of applications, ellipses are frequently seen in orbital mechanics, where planets and satellites follow elliptical paths around their focal points. On the other hand, helices are fundamental in the structure of DNA and other molecular formations, symbolizing the structural continuity in three dimensions.
Ellipses do not exhibit such uniformity in cross-sections, varying widely based on the angle of intersection with a plane.Interestingly, while ellipses can be graphed on a two-dimensional plane using Cartesian or polar coordinates, helices require three-dimensional space for accurate representation, typically described using parametric equations in three coordinates.
Comparison Chart
Dimensions
2D (two-dimensional)
3D (three-dimensional)
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Definition
A type of conic section
A type of spiral
Mathematical Basis
Sum of distances to foci is constant
Defined by radius and pitch
Representation
Cartesian or polar coordinates
Parametric equations
Applications
Orbital paths, lenses, architecture
DNA, springs, screws
Compare with Definitions
Ellipse
The shape formed by cutting a cone with an oblique plane that does not intersect the base.
The shadow of a circular disk can form an ellipse.
Helix
A three-dimensional spiral shape.
The staircase in the old lighthouse forms a tight helix.
Ellipse
A curve on a plane surrounding two focal points.
The garden's walking path is designed as a perfect ellipse.
Helix
Appears in architecture and art.
Modern sculptures often utilize the helical form for dynamic effect.
Ellipse
A locus of points that the sum of the distances to two fixed points is constant.
An ellipse can be drawn using two pins, a string, and a pencil.
Helix
Used in the design of coils and springs.
The metal coil in the mattress is a type of helix.
Ellipse
A geometric shape featuring an oval outline.
The planets orbit the sun in an elliptical path.
Helix
A curve defined by constant radius and pitch.
Industrial screws are designed as perfect helices for precise application.
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.
Helix
A helix (), plural helixes or helices (), is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis.
Ellipse
A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone.
Helix
(Mathematics) A three-dimensional curve that lies on a cylinder or cone, so that its angle to a plane perpendicular to the axis is constant.
Ellipse
The locus of points for which the sum of the distances from each point to two fixed points is equal.
Helix
A spiral form or structure.
Ellipse
Ellipsis.
Helix
(Anatomy) The folded rim of skin and cartilage around most of the outer ear.
Ellipse
(geometry) A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone. Category:en:Curves
Helix
(Architecture) A volute on a Corinthian or Ionic capital.
Ellipse
(grammar) To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.
In B's response to A's question:- (A: Would you like to go out?, B: I'd love to), the words that are ellipsed are go out.
Helix
To move or position (something) into the shape of a helix.
Ellipse
An oval or oblong figure, bounded by a regular curve, which corresponds to an oblique projection of a circle, or an oblique section of a cone through its opposite sides. The greatest diameter of the ellipse is the major axis, and the least diameter is the minor axis. See Conic section, under Conic, and cf. Focus.
Helix
To have the shape of a helix.
Ellipse
Omission. See Ellipsis.
Helix
To move along a helical course; spiral.
Ellipse
The elliptical orbit of a planet.
The Sun flies forward to his brother Sun;The dark Earth follows wheeled in her ellipse.
Helix
(mathematics) A curve on the surface of a cylinder or cone such that its angle to a plane perpendicular to the axis is constant; the three-dimensional curve seen in a screw or a spiral staircase. Category:en:Curves
Ellipse
A closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it;
The sums of the distances from the foci to any point on an ellipse is constant
Helix
(architectural element) A small volute under the abacus of a Corinthian capital.
Ellipse
Often used in optics and astronomy.
Many telescope mirrors are shaped as ellipses for better focus.
Helix
(anatomy) The incurved rim of the external ear.
Helix piercing
Helix
An upside down midair 360° spin in playboating.
Helix
To form or cause to form a helix.
Helix
A nonplane curve whose tangents are all equally inclined to a given plane. The common helix is the curve formed by the thread of the ordinary screw. It is distinguished from the spiral, all the convolutions of which are in the plane.
Helix
A caulicule or little volute under the abacus of the Corinthian capital.
Helix
The incurved margin or rim of the external ear. See Illust. of Ear.
Helix
A genus of land snails, including a large number of species.
Helix
A curve that lies on the surface of a cylinder or cone and cuts the element at a constant angle
Helix
A structure consisting of something wound in a continuous series of loops;
A coil of rope
Helix
Type genus of the family Helicidae
Helix
Found in nature in DNA and some proteins.
The double helix of DNA is a crucial element in genetic biology.
Common Curiosities
How is an ellipse different from a circle?
While both are round, an ellipse has two focal points, making it elongated, unlike a circle which is perfectly round with one central point.
What are the applications of a helix?
Helices are crucial in fields like genetics, mechanical engineering (springs and screws), and architecture.
How do mathematicians define an ellipse?
Mathematically, an ellipse is defined as the set of all points in a plane, the sum of whose distances to two fixed points (foci) is constant.
Can you describe the motion of an object following an elliptical path?
An object following an elliptical path orbits around two focal points, with its speed varying at different points along the orbit.
Can an ellipse be transformed into a helix?
No, an ellipse is a two-dimensional shape and cannot be transformed into a helix, which is three-dimensional, without adding an additional dimension.
Is a helix always three-dimensional?
Yes, by definition, a helix extends along three axes, making it inherently three dimesional.
What is an ellipse?
An ellipse is a regular oval shape, defined geometrically as the locus of points the sum of whose distances from two fixed points (the foci) is constant.
What is a helix?
A helix is a type of smooth space curve, like a spiraling spring, characterized by a constant radius from a central axis.
And a helix?
A helix is mathematically defined as a curve in three-dimensional space characterized by the property that the tangent line at any point makes a constant angle with a fixed line.
And the motion along a helical path?
An object moving along a helical path spirals around a central axis while simultaneously moving forward, creating a three-dimensional spiral shape.
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Written by
Maham Liaqat
Co-written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
