Geometric inequalities

Bonnesen's inequality

Bonnesen's inequality is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality. More precisely, consider a planar simple closed curve of length bounding a domain of area . Let and denote the radii of the incircle and the circumcircle. Bonnesen proved the inequality The term in the right hand side is known as the isoperimetric defect. Loewner's torus inequality with isosystolic defect is a systolic analogue of Bonnesen's inequality. (Wikipedia).

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Introduction to Differential Inequalities

What is a differential inequality and how are they useful? Inequalities are a very practical part of mathematics: They give us an idea of the size of things -- an estimate. They can give us a location for things. It is usually far easier to satisfy assumptions involving inequalities t

From playlist Advanced Studies in Ordinary Differential Equations

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Solving an absolute value inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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How to solve a one variable absolute value inequality or statement

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Solving an absolute value inequality by switching the signs

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Solving an absolute value inequality using an and compound inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Learn how to solve an graph an absolute value inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Solve and graph an absolute value inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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Solve and graph an absolute value inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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How to set up 2 cases to solve an absolute value inequality as a compound inequality

πŸ‘‰ Learn how to solve absolute value inequalities. The absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value inequality, we create the two cases of absolute value problems

From playlist Solve Absolute Value Inequalities

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How to Solve Inequalities (NancyPi)

MIT grad explains solving inequalities. This video focuses on solving linear inequalities. It shows when to switch the sign of the inequality, if you divide or multiply by a negative number, and is an introduction to how to solve inequalities in algebra. To skip ahead: 1) For a basic examp

From playlist Algebra

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Compound Inequalities 9 Examples including Fractions & Interval Notation

I start by defining Compound Inequalities & explaining the difference between "and" and "or" statements Inequality to Number Line examples at 2:03 7:01 8:44 Number Line to Inequality examples at 11:01 14:19 16:55 These examples include Interval Notation. Solving a Compound Inequality exa

From playlist Algebra 1

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Concentration of quantum states from quantum functional (...) - N. Datta - Workshop 2 - CEB T3 2017

Nilanjana Datta / 24.10.17 Concentration of quantum states from quantum functional and transportation cost inequalities Quantum functional inequalities (e.g. the logarithmic Sobolev- and PoincarΓ© inequalities) have found widespread application in the study of the behavior of primitive q

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

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Radek Adamczak: Functional inequalities and concentration of measure II

Concentration inequalities are one of the basic tools of probability and asymptotic geo- metric analysis, underlying the proofs of limit theorems and existential results in high dimensions. Original arguments leading to concentration estimates were based on isoperimetric inequalities, whic

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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Joe Neeman: Gaussian isoperimetry and related topics II

The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

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Lesson 12 Module 3 video

Grade 7: Module 3 Lesson 12 on Inequalities

From playlist Eureka Math Grade 7 Module 3

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What are compound inequalities

πŸ‘‰ Learn all about solving and graphing compound inequalities. An inequality is a statement in which one value is not equal to the other value. A compound inequality is a type of inequality comprising of more than one inequalities. To solve a compound inequality, we use inverse operations

From playlist Solve Compound Inequalities

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Minkowski's inequality

This is a basic introduction to Minkowski's inequality, which has many applications in mathematics. A simple case in the Euclidean space R^n is discussed with a proof provided.

From playlist Mathematical analysis and applications

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C73 Introducing the theorem of Frobenius

The theorem of Frobenius allows us to calculate a solution around a regular singular point.

From playlist Differential Equations

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Nexus Trimester - Randall Dougherty (Center for Communications Research)

Entropy inequalities and linear rank inequalities Randall Dougherty (Center for Communications Research) February 16, 2016 Abstract: Entropy inequalities (Shannon and non-Shannon) have been used to obtain bounds on the solutions to a number of problems. When the problems are restricted t

From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme

Related pages

Inequality (mathematics) | Loewner's torus inequality | Systolic geometry