Fun and Amazing Math

Some arguments that 0.999... equals 1, ranked from the one everybody posts first to the one that leaves no wiggle room at all, with a grade for how much work each proof actually does. Inspired by Vi Hart's classic "9.999... reasons that .999... = 1", one of the videos that shaped math YouTube. It is no longer on YouTube, but Vi Hart's whole catalog lives free at vimeo.com/vihart. CHAPTERS 0:00 The claim 0:12 Every argument, graded 0:48 Where the feeling comes from 1:37 Reason one: the thirds 2:34 Reason two: the 10x trick 3:58 Reason three: just subtract them 5:30 Reason four: no room between them 7:32 Reason five: what the dots mean 8:53 Reason six: the series 9:53 Reason seven: the same object 10:59 What to watch next This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #mathematics #brithemathguy

An infinite stack of square roots comes out to exactly 2, and the one line trick that gets you there is only valid once you show the tower settles on a number at all. CHAPTERS 0:00 - The tower, and the quick solve 0:53 - The same move proves 1 + 2 + 4 + 8 + ... = -1 2:01 - Checking the first few terms 2:35 - The bounded monotonic sequence criterion 3:00 - Proving the upper bound, then proving it increases 3:57 - The root that gets thrown out 4:19 - Swapping the 2 for any number 4:57 - The exponent version This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #mathematics #brithemathguy

A factorial is repeated multiplication and pi is a circle constant, so the two should have nothing to do with each other, but the moment you ask for the factorial of one half you get pi, and this video traces exactly where it enters: the Gamma function extends the factorial to every number, the factorial of one half turns out to be the area under a bell curve, and squaring that bell curve makes a perfectly round hill whose only clean integral is a full sweep around a circle. CHAPTERS 0:00 Pi is sitting in a factorial 0:42 Factorials only live on the whole numbers 1:23 The Gamma function 3:13 Everything collapses to one number 3:46 It turns into a bell curve 4:31 Where the pi comes from 6:16 The sweep that is 2 pi 6:36 Why it had to be pi 7:11 The answer 7:50 What to watch next This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #calculus #brithemathguy

If you would like to support my work, you can become a Youtube channel member. (click the Join button) CHAPTERS 0:00 The claim 0:11 Three observations, all of them true 0:38 The step that does not follow 0:57 A quartic can split into quadratics 1:09 Add 4x squared, then pay it back 1:36 A difference of squares appears 1:49 The two integer factors 2:07 The identity behind the move 2:26 What to watch next This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #algebra #brithemathguy

If you would like to support my work, you can become a Youtube channel member. (click the Join button) Given 2^x + 2^(-x) = 3, the exact value of 8^x + 8^(-x) falls out in three lines, and x never appears in the solution. CHAPTERS 0:00 The problem 0:19 Give it a name 1:03 It was never about x 1:15 Square it first 1:57 A bonus answer 2:07 Now cube it 2:50 The answer, and what x really is 3:10 The real lesson 3:22 What to watch next This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #algebra #brithemathguy

x with an x in its own exponent, equal to a power tower divided by 7^x. It looks like it needs the Lambert W function or a computer, but one early move collapses the whole thing into a clean integer answer. CHAPTERS 0:00 The problem 0:27 The trick, multiply by 7^x 0:43 Bring in logarithms 1:17 The guess, x equals 7^k 1:40 All integers now 2:07 The answer and the check 2:21 What to watch next This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #algebra #brithemathguy

100 factorial is a 158 digit monster, but two quick divisions reveal exactly how many zeros it ends in before you ever compute it. CHAPTERS 0:00 The problem 0:11 Feel how fast it grows 0:38 What a trailing zero really is 0:54 The real question, 2 times 5 pairs 1:07 Twos are everywhere, fives are rare 1:42 The first pass and the floor function 2:16 Why 20 is not the whole story 2:26 The 25s smuggle a second five 2:54 125 stops the count, the answer lands 3:16 The same trick on 1000! 3:40 A derivative factorials should not allow This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #numbertheory #brithemathguy

Try Brilliant's tutor for free: https://brilliant.org/BriTheMathGuy/ . You’ll also get 20% off an annual Premium subscription. You know the first and second derivatives, but with the Gamma function you can take half a derivative, and applying it twice gives back the ordinary one. CHAPTERS 0:00 - What lies between? 0:39 - A 300-year-old question 1:22 - The obvious guess 2:23 - Where coefficients come from 2:59 - Gamma to the rescue 3:33 - Taking half a derivative 4:47 - x squared, recovered 5:03 - Exponentials and sine 6:00 - The dial 6:27 - Nobody can draw it 7:08 - Riemann-Liouville 7:34 - The constant shock 7:57 - Fractional derivatives have memory 8:50 - Why anyone cares 9:17 - Today's sponsor: Brilliant 10:49 - The dial, recapped This video was partially created using Manim. This video was sponsored by Brilliant. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #mathematics #brithemathguy

A knight hopping a chessboard hides one of the hardest problems in computer science, and two crayon colorings settle it completely, from the 4x4 board that always strands you on square 15 to the magic square no knight's tour can ever draw. CHAPTERS 0:00 A tiny puzzle you cannot finish 0:46 The knight's tour, a monster in a chess costume 2:03 One knight move always flips the color 3:52 The open tour that really works 4:48 The balanced boards that still fail 6:25 Two colorings walk into a contradiction 8:24 The complete list of boards that work 9:30 Corners, and a greedy rule that wins 10:28 A magic square drawn by a knight 11:42 Where it finally breaks This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #chess #math #brithemathguy

If you would like to support my work, you can become a Youtube channel member. (click the Join button) This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #calculus #brithemathguy

A fraction that overflows your calculator turns out to equal 10^50 exactly, a 1 followed by fifty zeros. Here's the matching-exponents trick that collapses it by hand: factor 50 as 2 times 25, cancel the 25-powers, rewrite 2^50 as 4^25 to force the exponents to agree, and fuse 4 and 25 into 100. The whole thing was reverse-engineered so that 4 times 25 lands on 100, and 100^25 is just 10^50. This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #exponents #brithemathguy

Every circle is measured against pi, the ratio of circumference to diameter. But a circle is defined by its radius, not its diameter, and comparing the circumference to the radius gives tau = 2pi. This video walks through why tau is the more natural circle constant: a quarter turn is just tau/4, the area formula one-half tau r-squared honestly shows it came from an integral, and e^(i tau) = 1 is the full-rotation statement hiding behind Euler's identity. This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #tau #brithemathguy

A famous probability puzzle claims that switching between two sealed envelopes always nets you a 25% gain, and this video hunts down exactly where that airtight-looking reasoning quietly breaks. This video was partially created using Manim. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. #math #probability #brithemathguy

If you would like to support my work, you can become a Youtube channel member. (click the Join button) A drunk man wandering at random is guaranteed to find his way home, yet a drunk bird flying at random can be lost forever, and the whole difference comes down to whether one infinite series adds up to infinity. This video was partially created using Manim. #math #probability #brithemathguy

If you would like to support my work, you can become a Youtube channel member. (click the Join button) Six and seven sit one step apart on the number line, yet they could not be more different. Six rebuilds itself from its own divisors, while dividing 1 by 7 falls into the endlessly rotating number 142857 that snaps to 999999. Here is the math behind both, worked out step by step and checkable by hand.

The Dottie number: punch any number into your calculator, hit cos over and over, and you always spiral in to 0.7390851332... — a single fixed point that every starting value converges to. CHAPTERS 0:00 - Grab your calculator 0:40 - What's a fixed point? 1:54 - The cobweb diagram 3:15 - Why cosine squeezes distances 4:51 - Banach's Fixed-Point Theorem 6:21 - Why d is transcendental 7:25 - Who was Dottie? 8:04 - The bigger picture 8:53 - Outro This video was partially created using Manim. To learn more about animating with Manim, check out: https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

You've been told your whole life you can't divide by zero. But what actually goes wrong if you allow it? Walk through the logical consequences with a classic algebra proof that turns into a chain reaction — one seemingly-innocent step reveals how every number can equal every other number and the whole foundation of math falls apart. Plus what mathematicians do about it (L'Hôpital's rule, the Riemann sphere, projective geometry, wheel algebra). CHAPTERS 0:00 - The classic proof 1:00 - Where the knife went in 2:24 - The domino effect 3:05 - L'Hôpital's rule / the calculus escape hatch 4:25 - Undefined vs indeterminate 5:18 - The rebels: wheel algebra, Riemann sphere, projective geometry 7:16 - Why math said no 8:15 - Outro This video was partially created using Manim. To learn more about animating with Manim, check out: https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

e^π − π = 19.999... If you would like to support my work, you can become a Youtube channel member. (click the Join button) This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

This simple story about a barber destroyed the foundations of mathematics. The Barber's Paradox is more than just a riddle -- it's the glitch that proved logic itself was broken. In this video, we dive into Bertrand Russell's famous paradox, why it devastated the work of Gottlob Frege, and how it relates to the impossible "Set of all Sets". CHAPTERS 0:00 - Introduction 0:37 - The Barber's Rule 1:09 - Does the Barber Shave Himself? 1:50 - Why You Can't "Solve" It 2:24 - Russell's Paradox and Set Theory 3:33 - The Tragedy of Gottlob Frege 4:23 - How We Fixed It (ZFC) 4:54 - Conclusion This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) Is it deep math or just a cosmic accident? The equation π⁴ + π⁵ ≈ e⁶ is accurate to 0.00002. In this video, we investigate this bizarre numerical proximity and what it reveals about the nature of numbers. CHAPTERS 0:00 - The Equation 1:30 - How Close Is It? 3:00 - Visualizing the Error 5:00 - Other Famous Coincidences 7:00 - The Law of Small Numbers 8:30 - Conclusion This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #infinity This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #infinity This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #infinity This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #calculus This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Get a 7-day free trial and 25% off Blinkist Annual Premium by clicking: https://bit.ly/BriTheMathGuyMar24 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #number This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community This video was sponsored by Blinkist. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Get a 7-day free trial and 25% off Blinkist Annual Premium by clicking: https://bit.ly/BriTheMathGuyMar24 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #tetration Corrections: 4:11 x = e^W(ln4) (not just W(ln4)) This video was sponsored by Blinkist. This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #algebra This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #lambert This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) Are you fascinated by the enigmatic mathematical constant e? Ever wondered why it can't be written as a simple fraction? In this video, we'll dive into the elegant proof that demonstrates the irrational nature of e. Get ready to understand this mathematical marvel like never before! #math #brithemathguy #mathematics This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #mathematics This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Dive into the world of linear programming and discover the visual approach to solving optimization problems. Our latest tutorial breaks down the concept of feasibility regions and demonstrates how to graphically represent and interpret constraints within the context of maximizing productivity. Ideal for students and professionals in operations research and mathematics, this video offers a clear understanding of how to find the best solutions that adhere to given limitations. Learn the strategies behind effective decision-making and resource allocation, and see theory in action as we explore the practical applications of linear programming in everyday problem-solving. Tune in to unlock your potential in optimization techniques and decision sciences. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #linearprogramming This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Unlock the secrets of advanced mathematics comparing 1,000^999 to 999^1,000. Ideal for math Olympiad aspirants and enthusiasts, this tutorial delves into the intriguing world of exponential comparisons. Join us as we explore these colossal numbers, offering insightful analysis perfect for Olympiad training and mathematical challenges. Whether you're preparing for math competitions or simply love exploring complex mathematical concepts, this video is your gateway to understanding the nuances of exponentiation. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #matholympiadtraining This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #matholympiadtraining This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #lambert Corrections: 2:32 Of course x=3 is a solution :) This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Unlock the secrets of calculating logarithms by hand! Dive into Power Series and Simpson's Rule methods for an in-depth understanding of logarithmic math. Explore the convergence, accuracy, and practical applications of these fascinating techniques. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #logarithm This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Dive into the mystery of -1 factorial! Explore advanced math topics like integrals and complex numbers as we tackle this perplexing question. Meet the gamma function, the key to extending factorials beyond positive integers. But there's a twist—calculus shows the integral diverges to infinity. Is -1! factorial really infinity, or is it more complex? Unlock the secrets with analytic continuation and decode Wolfram Alpha's intriguing output. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #gamma This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Explore the enigmatic world of "Zero to the Power of i" with us! Dive into the complexities of exponentials, complex logarithms, and Euler's Formula as we challenge traditional mathematical norms. Is 0^i undefined, or is there more to the story? We'll use limits and polar forms to probe this mathematical mystery. If you're intrigued by complex numbers and mathematical tinkering, this video is for you. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join Corrections: 3:38 Note this is only true when x is a real number #math #brithemathguy #imaginarynumbers This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Explore the intriguing world of complex numbers as we unravel the mystery of the infinite power tower i^i^i^.... This video breaks down the mathematical journey step-by-step, from logarithmic properties, the Lambert W Function, and Newton's method to the surprising final solution. Discover the beauty and elegance of complex analysis in this engaging visual exploration. 🙏Support me by becoming a channel member! https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #imaginarynumbers This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Corrections: 1:04 Parenthesis are placed incorrectly - should be: i^{i^i^{i^...}} 6:55 The negative (-) sign should be inside the W function, next to ipi/2 9:25 Should have -ipi/2 for these, not just -pi/2 Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #math #brithemathguy #zerothroot This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

If you would like to support my work, you can become a Youtube channel member. (click the Join button) #ComplexNumbers #GammaFunction #brithemathguy This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

►SUPPORT ME BY BECOMING A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #algebratricks This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

►SUPPORT ME BY BECOMING A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #algebra This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Dive into the fascinating world of the Gamma Function (Γ(x)), the powerful generalization of the factorial function, with our captivating and visually stunning video! Explore the connection between derivatives, power rule, and factorials as we animate math concepts using Manim, making them easily digestible and engaging. We'll walk you through a step-by-step understanding of integral expressions, derivatives of power functions, and the relationship between the Gamma Function and factorials for both positive and negative real numbers. This video is perfect for students, teachers, and math enthusiasts alike, seeking to unravel the mysteries of advanced mathematical concepts. Don't miss out on this opportunity to expand your knowledge! ►WEBSITE https://www.brithemathguy.com ►SUPPORT ME BY BECOMING A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #gammafunction This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

Prepare to have your mind blown as we dive into the fascinating world of mathematics, exploring lesser-known facts and concepts that you won't find in a typical classroom. In this video, we'll uncover intriguing topics like palindromic numbers, spherical geometry, hyperbolic geometry, the Tower of Hanoi, the Mandelbrot Set, the Birthday Paradox, and more! ►WEBSITE https://www.brithemathguy.com ►BECOME A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #maths This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community. Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

In this video, we will discuss the concept of infinity to the power of 0. Contrary to popular belief, this mathematical expression is undefined, not equal to 1. While some may argue that it equals 1, the general consensus is that it cannot be defined due to the nature of infinity and its properties in exponentiation. Join me as we delve into the intricacies of this concept. ►WEBSITE https://www.brithemathguy.com ►BECOME A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #infinity This video was partially created using Manim. To learn more about animating with Manim, check out:https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

In this video, we explore the perplexing world of zero to the power of infinity. Is it equal to zero or does it approach infinity? To answer this question, we delve into the concept of limits and discuss how they relate to calculus, real analysis, and mathematical foundations. We also examine the properties of limits and apply them to various examples to gain a deeper understanding of this mysterious phenomenon. Along the way, we discover that the answer to zero to the power of infinity is not as straightforward as we might think and requires a nuanced understanding of mathematical principles. ►WEBSITE https://www.brithemathguy.com ►BECOME A CHANNEL MEMBER https://www.youtube.com/channel/UChVUSXFzV8QCOKNWGfE56YQ/join #math #brithemathguy #limits This video was partially created using Manim. To learn more about animating with Manim, check out: https://manim.community Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.