Daniel Hug: Random tessellations in hyperbolic space - first steps
Random tessellations in Euclidean space are a classical topic and highly relevant for many applications. Poisson hyperplane tessellations present a particular model for which mean values and variances for functionals of interest have been studied successfully and a central limit theory has
From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability
Solved simply: the impossible integral
Yes, it can't be done using substitution, by parts or changing variables (and using the Jacobian); but there is a very clever trick to actually compute this integral, which is attributed to Crofton, an English mathematician. This clever trick only requires the law of total expectation and
From playlist Novel topics (not in usual math curricula)
Understanding the discriminant as a part of the quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
How to solve a quadratic using the quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
The discriminant and finding the solutions using quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Andreas Bernig: Intrinsic volumes on pseudo-Riemannian manifolds
The intrinsic volumes in Euclidean space can be defined via Steinerโs tube formula and were characterized by Hadwiger as the unique continuous, translation and rotation invariant valuations. By the Weyl principle, their extension to Riemannian manifolds behaves naturally under isometric em
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Learn to find the solutions of a quadratic by applying the quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Solve a quadratic using the quadratic formula with complex answers
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Solving a quadratic using quadratic formula with two real solutions
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
How to use the quadratic formula to solve a quadratic equation
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Zakhar Kabluchko: Random Polytopes, Lecture III
In these three lectures we will provide an introduction to the subject of beta polytopes. These are random polytopes defined as convex hulls of i.i.d. samples from the beta density proportional to (1 โ โฅxโฅ2)ฮฒ on the d-dimensional unit ball. Similarly, betaโ polytopes are defined as convex
From playlist Workshop: High dimensional spatial random systems
Learn how to solve a quadratic equation using the quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Mark Meckes: Magnitude and intrinsic volumes in subspaces of L1
Magnitude is an isometric invariant of metric spaces, with origins in category theory, which turns out to be related to a wide variety of classical geometric invariants, including Minkowski dimension, volume, and surface measure. For convex bodies in ln1 , magnitude turns out to be an l1 a
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Herbert Edelsbrunner: The intrinsic volumes of a space filling diagram and their derivatives
The morphological approach to modeling the free energy in molecular dynamics by Roth and Mecke suggests to write it as a linear combination of weighted versions of the four intrinsic volumes of a space filling diagram: the volume, the area, the total mean curvature, and the total Gaussian
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Magenta: The colour that doesn't exist โ BBC REEL
When we look at a rainbow, we see a full spectrum of light. Every colour we could imagine. Except one โ magenta. Where is it? Well, officially magenta doesn't exist. There is no wavelength of light for magenta, meaning the human brain literally makes it up, but how? Video by Archie Croft
From playlist Reel Psychology
How does the discriminant relate to the quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
The little-known tree that revolutionised global communication โ BBC REEL
In Singapore, 1842, Dr William Montgomerie was shown a strange latex by his gardener. This material, when placed in hot water, could be moulded to any shape you wanted, and, on cooling, would set solid. You could do this again, and again and it would happily mould to any shape desired. Un
From playlist Reel Science
The surprising reason consciousness evolved โ BBC REEL
Every minute you spend awake, your mind passes from experience to experience. This ebb and flow of thoughts and feelings is often called a โstream of consciousnessโ โ and, throughout history, it was largely believed to only exist in humans. However, thanks to decades of consciousness resea
From playlist Reel Science
NERD WARS: Lara Croft Vs. Elektra!
Lara Croft Vs. Elektra ... who would win? Jeff and Adam debate the match-up in this week's episode of NERD WARS! Hear their weekly audio podcast: http://wackygamerpodcast.com/ Wackygamer on Facebook: http://www.facebook.com/pages/Cross-Platform-Comedy/75045579662 Vsauce on Faceb
From playlist Wackygamer
Describe and solve for the zeros using quadratic formula
๐ Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c