Geometric graphs | Intersection classes of graphs

Circular-arc graph

In graph theory, a circular-arc graph is the intersection graph of a set of arcs on the circle. It has one vertex for each arc in the set, and an edge between every pair of vertices corresponding to arcs that intersect. Formally, let be a set of arcs. Then the corresponding circular-arc graph is G = (V, E) where and A family of arcs that corresponds to G is called an arc model. (Wikipedia).

Circular-arc graph
Video thumbnail

What is the formula to determine the length of an arc

Learn how to solve problems with arcs of a circle. An arc is a curve made by two points on the circumference of a circle. The measure of an arc corresponds to the central angle made by the two radii from the center of the circle to the endpoints of the arc. The measure of the angle on a c

From playlist Circles

Video thumbnail

Learn to determine the length of an arc for a circle

Learn how to solve problems with arcs of a circle. An arc is a curve made by two points on the circumference of a circle. The measure of an arc corresponds to the central angle made by the two radii from the center of the circle to the endpoints of the arc. The measure of the angle on a c

From playlist Circles

Video thumbnail

What is the relationship for two inscribed angles with the same endpoints

Learn how to solve problems with arcs of a circle. An arc is a curve made by two points on the circumference of a circle. The measure of an arc corresponds to the central angle made by the two radii from the center of the circle to the endpoints of the arc. The measure of the angle on a c

From playlist Circles

Video thumbnail

Pendulum Motion

The Pendulum Motion Video Tutorial provides a wealth of details about the motion of a pendulum. Discussion topics include forces, free-body diagrams, force analysis with components, changes in speed and direction, position-time graphs, velocity-time graphs, changes in kinetic and potential

From playlist Vibrations and Waves

Video thumbnail

Find the central angle given the arc length and radius

👉 Learn how to solve problems with arc lengths. You will learn how to find the arc length of a sector, the angle of a sector, or the radius of a circle. An arc of a circle is the curve between a pair of points on the circumference of the circle. The angle of an arc is the angle subtended b

From playlist Solve Problems with Arc Length

Video thumbnail

Find the central angle given the arc length and radius

👉 Learn how to solve problems with arc lengths. You will learn how to find the arc length of a sector, the angle of a sector, or the radius of a circle. An arc of a circle is the curve between a pair of points on the circumference of the circle. The angle of an arc is the angle subtended b

From playlist Solve Problems with Arc Length

Video thumbnail

How to determine the measure of the arc if the chords are congruent

Learn how to solve problems with arcs of a circle. An arc is a curve made by two points on the circumference of a circle. The measure of an arc corresponds to the central angle made by the two radii from the center of the circle to the endpoints of the arc. The measure of the angle on a c

From playlist Circles

Video thumbnail

Given the radius and angle in degrees find the arc length

👉 Learn how to solve problems with arc lengths. You will learn how to find the arc length of a sector, the angle of a sector, or the radius of a circle. An arc of a circle is the curve between a pair of points on the circumference of the circle. The angle of an arc is the angle subtended b

From playlist Solve Problems with Arc Length

Video thumbnail

Using arc length formula to find the values for a circle

👉 Learn how to solve problems with arc lengths. You will learn how to find the arc length of a sector, the angle of a sector, or the radius of a circle. An arc of a circle is the curve between a pair of points on the circumference of the circle. The angle of an arc is the angle subtended b

From playlist Solve Problems with Arc Length

Video thumbnail

Given the radius of a circle find the length of an arc

Learn how to solve problems with arcs of a circle. An arc is a curve made by two points on the circumference of a circle. The measure of an arc corresponds to the central angle made by the two radii from the center of the circle to the endpoints of the arc. The measure of the angle on a c

From playlist Circles

Video thumbnail

Rainbows don't work the way you think they work

A visual explanation of the mathematics at the end of the rainbow. I learned this explanation from V.I. Arnold's book "Mathematical Understanding of Nature", where you can also find the calculations hidden behind these animations and graphs. https://bookstore.ams.org/mbk-85/ The rainbow

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Area of a Surface of Revolution Calculus 2

If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profrobbob This is the link to the lesson including all 3 examples https://www.youtube.com/watch?v=1T5O_5TmSZs&list=PL67C119EDA6BDE946&index=100 In this les

From playlist Calculus 2

Video thumbnail

Geometrical Snapshots from Ancient Times to Modern Times - Tom M. Apostol - 11/5/2013

The 23rd Annual Charles R. DePrima Memorial Undergraduate Mathematics Lecture by Professor Tom M. Apostol was presented on November 5, 2013, in Baxter Lecture Hall at Caltech in Pasadena, CA, USA. For more info, visit http://math.caltech.edu/events/14deprima.html Produced in association w

From playlist Research & Science

Video thumbnail

Area of a Surface of Revolution Calculus 1

In this lesson I explain the relationship between the lateral area of a right circular cone allows us to find the Area of a Surface of Revolution. Rule for Area of a Surface of Revolution at 16:37 , Example with a horizontal axis of rotation at 19:11 NOTE: at 19:44 I should say "2PI tim

From playlist Calculus

Video thumbnail

The Lost Fisherman Problem | What is the most efficient way back to shore?

STEMerch Store: https://stemerch.com/ Support the Channel: https://www.patreon.com/zachstar PayPal(one time donation): https://www.paypal.me/ZachStarYT Source: When least is best: https://amzn.to/2tL4svp Previous (optimization) video: https://youtu.be/6O8Jyrr9LRc â–ºFollow me Instagram: h

From playlist Puzzles

Video thumbnail

Jørgen Bang-Jensen: Antistrong digraphs

Jørgen Bang-Jensen: Antistrong digraphs An antidirected trail in a digraph is a trail (a walk with no arc repeated) in which the arcs alternate between forward and backward arcs. An antidirected path is an antidirected trail where no vertex is repeated. We show that one can decide in line

From playlist HIM Lectures 2015

Video thumbnail

Circle tangents, approx-areas and half-slopes | Algebraic Calculus One | Wild Egg

Having a technology for computing tangents to curves is very powerful. When applied to the unit circle, we get both inscribed and circumscribed polygonal spline approximations to the "area" of circular arcs, following the general plan of Archimedes. These are not true areas, but rather app

From playlist Algebraic Calculus One

Video thumbnail

When given the radius and angle, learn how to find the arc length

👉 Learn how to solve problems with arc lengths. You will learn how to find the arc length of a sector, the angle of a sector, or the radius of a circle. An arc of a circle is the curve between a pair of points on the circumference of the circle. The angle of an arc is the angle subtended b

From playlist Solve Problems with Arc Length

Related pages

Interval graph | Graph theory | Claw-free graph | Intersection graph | Journal of Combinatorial Theory | Vertex (graph theory) | Perfect graph | Operations research | Helly family