"I do math because once you prove a theorem, it stands forever."
"Szemeredi's theorem actually motivated a lot of subsequent research."
"The central limit theorem states that more samples lead to a distribution approximating normal."
"In any right angle triangle, the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle."
"Diagonalization is the essence of many theorems."
"Let me introduce you to something called the Pythagorean theorem my friend. A squared plus B squared squared."
"It's just Pythagoras theorem souped up to three dimensions."
"This result is probably the most famous of all mathematical theorems."
"This is the theorem we're going to use, and if you look in your online lecture notes H you'll see a sketch of the proof if you're interested."
"Bayes theorem is a math formula for determining conditional probability."
"Bayes theorem says that for any two events A and B, the probability of A given B equals the probability of B given A."
"The big bang that started the subject was an impossibility theorem."
"If a positive integer p is prime, then so is 2p + 1."
"If a positive integer n has remainder 1 when divided by three, then n cubed also has remainder 1 when divided by three."
"The Pythagorean theorem solves the problem of computing diagonal distance."
"Angles on a straight line sum to 180 degrees."
"Gauss's divergence theorem is an extremely powerful equality in vector calculus."
"The phrase 'if thenism' is used by these people to denote the view that all theorems are logical, reliable, objective conclusions, deductions from their axioms."
"Pythagoras is most well known in math class for the Pythagorean theorem."
"From Mozlas Theorem: A Genetic Approach to Algebraic Number Theory by H.M Edwards. H.M Edwards is another one of these mathematicians who appreciates that you should learn about the development of a subject, not how it was written afterwards."
"Erin Fest's theorem allows us to make a direct connection between the classical and the quantum worlds."
"Central Limit Theorem concludes that the sampling distributions are helpful in dealing with non-normal data."
"The theorem states something remarkably useful."
"So, actually, the theorem applies to power series and lots of other things too."
"Now, we've got Pythagoras' theorem and we worked out this length and this length we can work out the hypotenuse."
"The thing with Pythagoras is Steven my thigh grasses theorem only works in right angle triangles."
"So these are what are known as Pythagorean triples if you have a right triangle with sides a B and C then there's a famous theorem called the Pythagorean theorem that says a squared plus B squared is equal to C squared."
"A famous example of that is sometimes called Fermat's Last Theorem although clearly it wasn't a theorem it was a conjecture which is trying to generalize Pythagorean triples to powers greater than 2."
"X plus Y equals 180. That's the straight line, that's the diameter."
"The angle made at the circumference in a semicircle is a right angle."
"The angle subtended at the center of the circle is twice the angle subtended at the circumference via the same arc."
"Opposite angles in a cyclic quadrilateral add up to 180."
"Now obviously what we're looking at is the alternate segment theorem so we're looking at this angle here being equal to the total angle just there."
Theorems: "Mean value theorem tells you that there's a point where the slope of the tangent line matches the slope of the secant line."
"The Pythagorean theorem: a² + b² = c²."
"The Pythagorean theorem: a squared plus b squared equals c squared."
"Proofs could be a string of symbols that mechanically certifies a theorem is true."
"The main idea is something called the fundamental theorem of algebra. The degree of the polynomial is how many solutions we will have."
"The Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse of a right triangle."
"Welcome back, so I'm really excited today to tell you about the Shannon Nyquist sampling theorem."
"That's one of those wonderful theorems that makes your heart happy."
"So the answer is yes, it's that's called the chronic of a burr theorem."
"The program is the proof of its type; the type is the theorem."
"Imagine for a second if the Pythagorean theorem, known and proved since ancient times, were believed but eluded proof until today."
"The basic idea behind the Central Limit Theorem is this: let's say we collect samples of size n from a population and then we calculate the mean of each of those samples and then plot those means on a histogram, the histogram will approximate a normal distribution."
"Cauchy's residue theorem is perhaps the most fundamental result in complex analysis."
"Transformations are used all the time and they are also very nicely contained in the proof of Sklar's theorem."
"So it's intermediate value theorem, intermediate value theorem."
"D'Morse theorem essentially allows us to take the power of complex numbers and the roots of complex numbers."
"The square of the hypotenuse of a right-angle triangle is equal to the sum of the squares of the other two sides."
"Whenever a radius and a tangent to a circle intersect, they form a right angle."
"The residue theorem, this is probably one of the most important formulas when you're studying complex analysis."
"Pythagoras's Theorem says a squared plus b squared equals c squared."
"Every polynomial equation of degree n has n complex solutions."
"A theorem is a statement of fact that's known to be true."
"A lemma is like a theorem in that it's something that's true and it's proved with a proof."
"The central limit theorem states that the distribution of many sample means will be normally distributed, even if the underlying data being sampled from is not normally distributed."
"We can use Pythagoras for this, can't we?"
"The most beautiful theorem in computer science, my goodness..."
"Using the fundamental theorem of calculus, we know that this is equal to \( F(2) - F(0) \)."
"Wilson's theorem tells us that p minus 1 factorial is congruent to minus 1 mod p."
"Intermediate Value Theorem requires that the function is continuous."
"The central limit theorem says the means drawn from multiple samples of the data when plotted will resemble a bell-shaped normal curve."
"The fundamental theorem of arithmetic states that every positive integer has a unique factorization into its prime factors."
"The central limit theorem says that this is how the world works, so you get to use the standard error, and you get to do these kinds of calculations."
"Remember Pythagoras' theorem? C squared is equal to A squared plus B squared."
"The hypotenuse squared is always equal to the sum of the other two square sides."
"A theorem has two parts: the hypothesis, what you're given, and the conclusion, what you have to prove."
"The central limit theorem tells us that no matter what the population looks like, if your samples are big enough, then the sampling distribution will be normal."
"The Gerschgorin theorem is quite neat, I will say."
"The Axiom of Choice is certainly very convenient and it makes a lot of results simpler to state."
"This is Euler's beautiful proof of this theorem."
"No matter what right triangle you have, if you add up the squares of these legs, it will equal the square of that hypotenuse."
"A theorem is a statement that has been proved."
"That's the side splitter theorem, that when you draw a line parallel to one of the sides of the triangle and it goes through the other two sides, it's going to cut the triangle proportionally."
"So this is a theorem, let's see what it looks like."
"The circulation is important because of a powerful theorem which Lord Kelvin evolved from the dynamical laws of motion."
"These two concepts are linked by Stoke's theorem, which says something similar to the fundamental theorem of calculus."
"Theorems are true, well they've been proven to be true."
"The mean value theorem was essential to this and proves that previous theorem."
"This is the famous Binomial Theorem."
"The central limit theorem applies to any statistic."
"Pythagoras is the great leveler of mathematics."
"If you understand that you can inscribe this right triangle on a circle with this particular radius, we can always use the Pythagorean theorem."
"Parallel axis theorem is very important."
"It's a really important theorem of algebra."
"I'm going to say this is the three theorem Sudoku puzzle."
"This is known as Theorema Egregium, Latin for 'The Remarkable Theorem'."
"The Cauchy-Goursat theorem is a really important ramification of this."
"The Pythagorean theorem, a² + b² = c², is extremely important in all levels of mathematics, especially geometry."
"The Pythagorean theorem says \( x^2 + y^2 = r^2 \) or \( r \) is the square root of \( x^2 + y^2 \)."
"To calculate the resultant displacement, we could simply use the Pythagorean theorem."
"So the magnitude is simply going to be the use of Pythagoras's theorem."
"The Nyquist Sampling Theorem states you've got to go ahead and sample something at least twice the frequency at which it is naturally occurring."
"This work energy theorem... that's an important one for the week."
"That's a second little lemma or theorem that you must know in order to do statistical mechanics."
"Wilson's theorem: that P minus 1 factorial is congruent to minus 1 mod p."
"This is one of the most useful theorems you will ever see."
"Because M is the perpendicular bisector of segment AB, triangle APC is congruent to triangle BPC by the side angle side theorem."
"Simon's theorem of five in the middle always leads to an interesting puzzle."
"Magnetization cannot be understood in classical terms; there is actually a theorem that says that magnetization is zero for any classical system."
"By the principle of mathematical induction, the theorem is true for all N in the natural numbers."
"Superposition theorem is actually one of my favorite electronics theorems because it's no duh, the effects add up."
"Steady-state error we can meet pretty easily because we use the final value theorem."
"The formula for Pythagoras is a squared plus b squared equals c squared."
"Any point that lies on the perpendicular bisector of a line segment should be equidistant from the two endpoints of that line segment."
"If the proof of a theorem is not immediately apparent, it may be because you are trying the wrong approach."
"So that's the fundamental theorem of calculus."
"That's the fundamental theorem of calculus."
"The Pythagorean theorem is screaming in your head."
"The square of the hypotenuse is equal to the sum of the squares of the other two sides."
"Any triangle inscribed in a semicircle with a diameter as one side is a right triangle."
"Pythagoras: A squared plus B squared equals C squared is right."
"The Fundamental Theorem of Calculus states this."
"Theorems are the discoveries we make in our journey throughout the world of mathematics."
"Once we've proven a theorem, sometimes a number of other results follow very easily from it."
"The fundamental theorem of numerical analysis: stability holds if and only if convergence holds."
"The Jordan Curve Theorem is a very cool theorem."
"That's what we want to find. How do we get it? Again, we apply Pythagoras' theorem."
"Pythagoras theorem applies because this is a right-angled triangle."
"Parseval's relation for a continuous time signal."
"With the Lebesgue integral, we have this amazing theorem called the Dominated Convergence Theorem."
"The sum of the squares of the two legs equals the square of the hypotenuse."
"This is actually called momentum integral theorem which is a very important theorem in boundary layer analysis."