Theorems in Riemannian geometry
In Riemannian geometry, the Rauch comparison theorem, named after Harry Rauch, who proved it in 1951, is a fundamental result which relates the sectional curvature of a Riemannian manifold to the rate at which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend to spread. The statement of the theorem involves two Riemannian manifolds, and allows to compare the infinitesimal rate at which geodesics spread apart in the two manifolds, provided that their curvature can be compared. Most of the time, one of the two manifolds is a "comparison model", generally a manifold with constant curvature , and the second one is the manifold under study : a bound (either lower or upper) on its sectional curvature is then needed in order to apply Rauch comparison theorem. (Wikipedia).
Learning to evaluate the sum of two angles in radians, tan
π Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Using the addition of two angles formula and sine
π Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
D-Day - The German Counterattack 1944
Find out what happened when the Germans counterattacked the Allied landing beaches on 6 June 1944, with surprising and potentially devastating results. Enjoy reading, then check out my latest book, The Bridge Busters: The First Dambusters and the Race to Save Britain https://www.amazon.c
From playlist Battle of Normandy 1944
Evaluate the difference of two angles for sine
π Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
Jeffrey Achter, Equidistribution counts abelian varieties
VaNTAGe Seminar, February 22, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk are listed below. Sutherland: https://arxiv.org/abs/1604.01256 Gekeler: https://academic.oup.com/imrn/article/2003/37/1999/863196 Job Rauch: https://www.universiteitleiden.nl/binar
From playlist Curves and abelian varieties over finite fields
Determining the sine of the sum of two angles
π Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
Einstein's Quantum Riddle | Full Documentary | NOVA | PBS
Join scientists as they grab light from across the universe to prove quantum entanglement is real. #NOVAPBS Official Website: https://to.pbs.org/3vqiMpg Einstein called it βspooky action at a distance,β but today quantum entanglement is poised to revolutionize technology from computers t
From playlist Full episodes I NOVA
Using sum of two angles to evaluate an angle in radians for tangent, tan
π Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
Using difference of two angles with tangent to evaluate
π Learn how to evaluate the tangent of an angle in degrees using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
2.2 Wie finanziert sich "Linux"
From playlist Linux fΓΌr Alle
Harsha Hutridurga: A new approach to study strong advection problems
The lecture was held within the framework of the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. (16.02.2017) In this talk, I shall be attempting to give an overview of a new weak convergence type tool developed by myself, Thom
From playlist HIM Lectures: Trimester Program "Multiscale Problems"
Radian Measure (Mini Lesson) - Algebra 2
http://www.youtube.com/vinteachesmath This video provides a mini lesson on the concept of radian measure. In particular, this video shows how the unit circle, circumference, and degree measure of an angle can be used to explain the concept of radian measure. This video is appropriate fo
From playlist Trigonometry (old videos)
ExtremwetterschΓ€den: Wer trΓ€gt die Verantwortung?
Max-Planck-Forum in Kooperation mit dem Max-Planck-Institut fΓΌr Sozialrecht und Sozialpolitik Aufzeichnung vom 15.11.2022 Auf dem Podium: Prof. Dr. Ulrich Becker, Direktor am Max-Planck-Institut fΓΌr Sozialrecht und Sozialpolitik Ernst Rauch, Chief Climate and Geo Scientist, Munich Re Dr
From playlist Videos auf Deutsch
How to evaluate using the sum of two angles for sine
π Learn how to evaluate the sine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all th
From playlist Sum and Difference Formulas
Pre-Calculus - Using the difference of two angles to evaluate the an angle for cosine, cos195
π Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
The Geometry of Hilbert's 13th problem - Jesse Wolfson
Special Seminar on Hilbert's 13th Problem I Topic: The Geometry of Hilbert's 13th problem Speaker: Jesse Wolfson Affiliation: University of California, Irvine Date: December 5, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Alexandra SHLAPENTOKH - Defining Valuation Rings and Other Definability Problems in Number Theory
We discuss questions concerning first-order and existential definability over number fields and function fields in the language of rings and its extensions. In particular, we consider the problem of defining valuations rings over finite and infinite algebraic extensions
From playlist Mathematics is a long conversation: a celebration of Barry Mazur
GCSE Science Revision Chemistry "NPK Fertilisers" (Triple)
Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at how NPK fertilisers are produced. Deliberate Thought by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/) Source:
From playlist 9-1 GCSE Chemistry Paper 2 Resources
Using sum and difference formula to find the exact value with cosine
π Learn how to evaluate the cosine of an angle in radians using the sum/difference formulas. To do this, we first express the given angle as a sum or a difference of two (easy to evaluate) angles, then we use the unit circle and the Pythagoras theorem to identify the angles and obtain all
From playlist Sum and Difference Formulas
The Most Efficient Way to Destroy the Universe β False Vacuum
What if there is a way to destroy the universe so fundamentally that life as we know it will be impossible forever? OUR CHANNELS ββββββββββββββββββββββββββ German Channel: https://kgs.link/youtubeDE Spanish Channel: https://kgs.link/youtubeES HOW CAN YOU SUPPORT US? βββββββββββββββββ
From playlist The Existential Crisis Playlist