Theorems in geometry | Theorems in algebra | Trigonometry | Rational numbers
In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: In radians, one would require that 0 ≤ x ≤ π/2, that x/π be rational, and that sin x be rational. The conclusion is then that the only such values are sin 0 = 0, sin π/6 = 1/2, and sin π/2 = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. The theorem extends to the other trigonometric functions as well. For rational values of θ, the only rational values of the sine or cosine are 0, ±1/2, and ±1; the only rational values of the secant or cosecant are ±1 and ±2; and the only rational values of the tangent or cotangent are 0 and ±1. (Wikipedia).
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
Duality Theorem In this video, I use a neat little trick to show that the limit as n goes to infinity of 2^n is infinity, by using the fact (shown before) that the limit of (1/2)^n is 0. Exponential Limit: https://youtu.be/qxlSclbmh-w Other examples of limits can be seen in the playlis
From playlist Sequences
Calculus 5.3 The Fundamental Theorem of Calculus
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1
I show how the Definition of Area of a Plane is a special case of the Riemann Sum. When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal. I work through two examples that are rela
From playlist Calculus
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
Proving Pi Is Irrational - What You Never Learned In School!
Happy Pi Day (3/14)! Everyone knows that pi is an irrational number, but how do you prove it? This video presents one of the shortest proofs that pi is irrational, and the proof requires only high school calculus to understand. Niven's proof http://www.ams.org/journals/bull/1947-53-06/S00
From playlist Pi
Simplify the Negation of Statements with Quantifiers and Predicates
This video provides two examples of how to determine simplified logically equivalent statements containing quantifiers and predicates. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Learn more math and science with brilliant.org, https://brilliant.org/blackpenredpen/ , first 200 people to sign up will get 20% off your subscription, and you can support my channel, too! Thank you! Proving sqrt(2) is irrational by using the Rational Zeros Theorem, https://youtu.be/ao6
From playlist [Math For Fun] Brilliant Problems
Michio Kaku Explains String Theory | Big Think
Michio Kaku Explains String Theory New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- The co-founder of Field String Theor
From playlist The universe explained | Big Think
Michio Kaku: The Universe Is a Symphony of Vibrating Strings | Big Think
Michio Kaku: The Universe Is a Symphony of Vibrating Strings New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- The co-fou
From playlist The universe explained | Big Think
The Field With One Element and The Riemann Hypothesis (Full Video)
A crash course of Deninger's program to prove the Riemann Hypothesis using a cohomological interpretation of the Riemann Zeta Function. You can Deninger talk about this in more detail here: http://swc.math.arizona.edu/dls/ Leave some comments!
From playlist Riemann Hypothesis
Michio Kaku: The Dark Side of Technology | Big Think
What is the most dangerous technology? New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Michio Kaku explores the dark si
From playlist Inventing the Future | Big Think
Michio Kaku: The Holy Grail of Planetary Astronomy | Big Think
The Holy Grail of Planetary Astronomy New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- The co-founder of Field String Th
From playlist Earth and Beyond | Big Think
The precise definition of the limit EXPLAINED! (KristaKingMath)
► My Limits & Continuity course: https://www.kristakingmath.com/limits-and-continuity-course The precise definition of the limit, also called the epsilon-delta definition, is the proof of the concept of the limit. It proves the limit because it shows how, as you move closer and closer to
From playlist Calculus I
Michio Kaku forecasts the future of space travel
New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- The co-founder of Field String Theory explains why the universe has
From playlist Journey to outer space | Big Think
Michio Kaku: String Theory Is The Only Game In Town | Big Think
Michio Kaku: String Theory Is The Only Game In Town New videos DAILY: https://bigth.ink Join Big Think Edge for exclusive video lessons from top thinkers and doers: https://bigth.ink/Edge ---------------------------------------------------------------------------------- The co-founder of
From playlist Earth and Beyond | Big Think
LIGHTS, CAMERA, ACTION! - FILM MONTH ON BRITISH PATHÉ (FEBRUARY 2016): Special Report: On Set. With so many starry clips from the Golden Age of the Silver Screen to choose from, we've had to create more videos this month than usual. So in this extra long, 20 minute "Special Report", we v
From playlist Special Reports | British Pathé
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Introduction to number theory lecture 1.
This lecture is the first lecture of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 This lecture gives a survey of some of the topics covered later in the course,
From playlist Introduction to number theory (Berkeley Math 115)