Articles containing proofs | Theorems in topology | Theorems in measure theory

Ham sandwich theorem

In mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide each one of them in half (with respect to their measure, e.g. volume) with a single (n − 1)-dimensional hyperplane. This is even possible if the objects overlap. It was proposed by Hugo Steinhaus and proved by Stefan Banach (explicitly in dimension 3, without taking the trouble to state the theorem in the n-dimensional case), and also years later called the Stone–Tukey theorem after Arthur H. Stone and John Tukey. (Wikipedia).

Ham sandwich theorem
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The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously

Ham sandwiches are delicious, but they’re also pretty useful when it comes to understanding the universe. Is Anything Truly Random? - https://youtu.be/tClZGWlRLoE Read More: The Ham Sandwich Theorem Is a Delicious and Puzzling Mathematical Principle https://curiosity.com/topics/the-ham

From playlist Elements | Seeker

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Calculus - The sandwich theorem

This video explains more about the sandwich theorem and how we use it to find the limit of a function. This theorem is also known as the squeeze theorem. For more videos visit http://www.mysecretmathtutor.com

From playlist Calculus

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Topology is weird: The Ham Sandwich Theorem

Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. Today we talk about my favourite math theorem: the Ham Sandwich theorem. Consider a sandwich with three components. Then the theorem cla

From playlist Cool Math Series

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AlgTop14: The Ham Sandwich theorem and the continuum

In this video we give the Borsuk Ulam theorem: a continuous map from the sphere to the plane takes equal values for some pair of antipodal points. This is then used to prove the Ham Sandwich theorem (you can slice a sandwich with three parts (bread, ham, bread) with a straight planar cut

From playlist Algebraic Topology: a beginner's course - N J Wildberger

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The Squeeze Theorem

This video explains the Squeeze (Sandwich) Theorem and provides an example. http://mathispower4u.com

From playlist Calculus Proofs

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Calculus - Use the sandwich theorem to find the limit

This video shows an example of using the sandwich theorem to find the limit of a function. This theorem is also called the squeeze theorem. For more videos visit http://www.mysecretmathtutor.com

From playlist Calculus

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The Ham Sandwich theorem and the continuum | Algebraic Topology | NJ Wildberger

We discuss the Borsuk-Ulam theorem concerning a continuous map from the sphere to the plane, and the Ham Sandwich theorem. One application is to show that the two dimensional and three dimensional affine spaces are not homeomorphic. This is the 14th lecture of this beginner's course in Al

From playlist Algebraic Topology

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Ham Sandwich Problem - Numberphile

This video features Dr Hannah Fry (more links below) ↓↓↓ Check out Brilliant.org: https://brilliant.org/numberphile (20% off premium subscription) That circle cutting problem on Brilliant: https://brilliant.org/NumberphileSandwich Hannah Fry on Twitter: https://twitter.com/FryRsquared R

From playlist Women in Mathematics - Numberphile

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What is Special About Polynomials? (Perspectives from Coding theory and DiffGeom) - Larry Guth

What is Special About Polynomials? (Perspectives from Coding theory and Differential Geometry) Larry Guth Massachusetts Institute of Technology March 13, 2013 olynomials are a special class of functions. They are useful in many branches of mathematics, often in problems which don't mention

From playlist Mathematics

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The Codimension Barrier in Incidence Geometry - Larry Guth

Larry Guth Massachusetts Institute of Technology March 14, 2013 Incidence geometry is a part of combinatorics that studies the intersection patterns of geometric objects. For example, suppose that we have a set of L lines in the plane. A point is called r-rich if it lies in r different lin

From playlist Mathematics

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An isoperimetric inequality for the Hamming cube and some consequences - Jinyoung Park

Computer Science/Discrete Mathematics Seminar I Topic: An isoperimetric inequality for the Hamming cube and some consequences Speaker: Jinyoung Park Affiliation: Rutgers University Date: November 18, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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Johnathan Bush (7/8/2020): Borsuk–Ulam theorems for maps into higher-dimensional codomains

Title: Borsuk–Ulam theorems for maps into higher-dimensional codomains Abstract: I will describe Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Given a continuous map from a sphere to Euclidean space, we say the map is odd if it respects the standard antipodal

From playlist AATRN 2020

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The pancake theorem

Making a single pancake is one thing, but being able to cut it exactly in half with a single straight line is a whole new ball game. This time, we will see that not only this is possible, you can actually cut two pancakes simultaneously with a single straight line, and see a little bit the

From playlist Summer of Math Exposition 2 videos

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The sequence that grows remarkably large, then drops to zero!

Goodstein sequences can get larger than Graham's number and the growth rate can be faster than Ackermann’s function. In fact, these sequences grow at such an incredible rate, that the theorem literally cannot be proven using first order arithmetic and can only be proven using a stronger sy

From playlist Summer of Math Exposition 2 videos

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Proof: The Angle Bisector Theorem

This video states and proves the angle bisector theorem. Complete Video List: http://www.mathispower4u.yolasite.com

From playlist Relationships with Triangles

Related pages

Outer measure | PPA (complexity) | Finite set | Unit sphere | Continuous function | Intermediate value theorem | Origin (mathematics) | Big O notation | Dimension | Hyperplane | Stefan Banach | Squeeze theorem | Linear continuum | Point (geometry) | Mathematics | Function (mathematics) | Sphere | Euclidean space | Borsuk–Ulam theorem | Moment curve | N-sphere | Subset | Counting measure | Linear combination | Discrete & Computational Geometry | Equivariant topology | Discrete geometry | Computational geometry | Necklace splitting problem | Fair cake-cutting | Measure (mathematics) | Exact division | Orientation (geometry) | Hugo Steinhaus | Algorithm | John Tukey | Stanislaw Ulam | Robertson–Webb rotating-knife procedure