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35edited Jun 7, 2021 at 19:32When you have three side lengths satisfying a ≤ b ≤ c and the sum a + b = c, then the triangle is degenerate.
(Valid triangles have a + b > c and triangles with a + b < c are not possible.)
Content Under CC-BY-SA license Degeneracy (mathematics) - Wikipedia
A degenerate conic is a conic section (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.
• A point is a degenerate circle, namely one with radius 0.
• The line is a degenerate case of a parabola if the parabola resides on a tangent plane. In inversive geometry, a line is a degenerate case of a circle, with infinite radius.Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 6 mins
Degenerate Triangles - YouTube
Degenerate Polygons - The Math Doctors
Mar 4, 2022 · Degenerate Triangle If a degenerate triangle is a triangle whose three vertices are collinear, is it not then just a straight line? I'm having some difficulty picturing a "triangle" with …
Degenerate triangle. Property of a degenerate triangle
Definition of a degenerate triangle: A degenerate triangle is a triangle in which all three vertices lie on the same straight line. All other triangles are non-degenerate.
inequality - Why invent the concept of degenerate triangle ...
Mar 19, 2023 · I've come across the term "degenerate triangles" in my studies of mathematics and geometry, and I'm curious about why this concept was invented. From what I understand, a …
2.4: Straight angle - Mathematics LibreTexts
A triangle is degenerate if and only if one of its angles is equal to \(\pi\) or 0. Moreover in a degenerate triangle the angle measures are 0, 0, and \(\pi\).
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Degenerate | Glossary | Underground Mathematics
In mathematics, something is called degenerate if it is a special case of an object which has, in some sense, “collapsed” into something simpler. For example: A degenerate triangle has all …
4.4: Side-Side-Side condition - Mathematics LibreTexts
Let \(\triangle ABC\) be a nondegenerate triangle and let \(f\) be a motion of the plane such that \(f(A) = A\), \(f(B) = B\) and \(f(C) = C\). Show that \(f\) is the identity map; that is, \(f(X) = X\) for any point \(X\) on the plane.
Mathematics For Blondes: Degenerate triangle
Mar 28, 2016 · A degenerate triangle - is the lower limit of the application of the law of cosines. After that we will look at the law of cosines in general.
Degenerate and Non Degenerate Triangles - YouTube
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The converse of this theorem is also true. That is if ∆A’B’C’ is degenerate then P must lie on the circumcircle of ∆ABC. Choose P on the circumcircle of ∆ABC. Let Q be the intersection of the …
Degenerate - Mathwords
A degenerate triangle is the "triangle" formed by three collinear points. It doesn’t look like a triangle, it looks like a line segment. A parabola may be thought of as a degenerate ellipse with …
Triangle inequality | Theorem, Geometry, & Degenerate | Britannica
triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. (In cases where a + b = c , a …
Pythagoras's Inequalities ‹ OpenCurriculum
If you try to cut the length of the hypotenuse at one end of the hypotenuse, you will form a degenerate triangle unless you pull the two legs closer together, thus shrinking the angle in …
ELI5 What are degenerate cases and trivial cases?
Degenerate cases are cases that are special, require special handling because the usual assumptions fail, and simplify the situation in certain way. For example, if you have 3 points on …
Triangle Inequality | Brilliant Math & Science Wiki
The triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side. It follows from the fact that a straight line is the shortest …
What are degenerate polygons? - Computer Science Stack …
Feb 16, 2015 · A polygon is degenerate if some of its vertices lie on each other. e.g the triangle (0,0),(0,1),(0,0) is degenerate. It has 3 sides, and 3 vertices, but two of vertices repeat. It's …
Nondegenerate triangle of zero area. How is it possible?
Oct 10, 2023 · In standard analysis, such a triangle must have non-zero area, but on this page we are accepting many things that are impossible in standard analysis, such as two points that …
Khan Academy
Learn about the triangle inequality theorem in this Khan Academy video.
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