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Think Twice
United States
Приєднався 16 січ 2017
Mathematics in motion.
Generating Conic Sections with Circles | Part 3. The Hyperbola
Learn mathematics in a fun and interactive way at:
brilliant.org/ThinkTwice
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Help me create more videos by supporting Think Twice on:
► Patreon: patreon.com/Think_twice
► Twitter: thinktwice2580
► Instagram: thinktwice_ltu
(@thinktwice_ltu)
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Contact me:
► thinktwiceask@gmail.com
brilliant.org/ThinkTwice
-----------------------------------------------------------------------------------------------------------
Help me create more videos by supporting Think Twice on:
► Patreon: patreon.com/Think_twice
► Twitter: thinktwice2580
► Instagram: thinktwice_ltu
(@thinktwice_ltu)
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Contact me:
► thinktwiceask@gmail.com
Переглядів: 26 427
Відео
Generating Conic Sections with Circles | Part 2. The Parabola
Переглядів 26 тис.3 роки тому
Strengthen your problem-solving skills at: brilliant.org/ThinkTwice Let C be a circle centered at F and let L denote a line on the same plane as C which doesn't intersect C. Then construct a variable circle tangent to L and C and denote its center as X. A collection of all such possible centers X is a parabola. Help me create more videos by supporting the channel on: ► Patreon: patreon.com/Thin...
Generating Conic Sections with Circles | Part 1. The Ellipse
Переглядів 37 тис.3 роки тому
Learn key problem-solving techniques at: brilliant.org/ThinkTwice Take any circle and pick any one of its interior points. Then the collection of the centers of circles passing through that point and tangent to the initial circle is an ellipse. Help me create more high-quality videos by supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktw...
Euler's Formula V - E + F = 2 | Proof
Переглядів 55 тис.4 роки тому
Explore the world of 3-dimensional geometry by signing up for free at: brilliant.org/ThinkTwice Proofs for two theorems used in this video: ► Polygon triangulation: ua-cam.com/video/2x4ioToqe_c/v-deo.html ► Area of a spherical triangle: ua-cam.com/video/Y8VgvoEx7HY/v-deo.html Euler's polyhedron formula is one of the simplest and beautiful theorems in topology. In this video we first derive the ...
Every Polygon can be Triangulated Into Exactly n-2 Triangles | Proof by Induction
Переглядів 45 тис.4 роки тому
Learn more about propositional logic and dive into the world of beautiful geometry at: brilliant.org/ThinkTwice Help me create more content by supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktwice2580) ► Instagram: thinktwice_ltu (@thinktwice_ltu) Contact me: ► thinktwiceask@gmail.com 🎵 Music by : Jonkyoto - www.fiverr.co...
Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle
Переглядів 65 тис.4 роки тому
For more fun and challenging 3D geometry problems head to: brilliant.org/ThinkTwice Please consider supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktwice2580) ► Instagram: thinktwice_ltu (@thinktwice_ltu) Summary: ► A spherical triangle is a surface area of a sphere bounded by 3 arcs of great circles. ► Any spherical tria...
The Fermat Point of a Triangle | Geometric construction + Proof |
Переглядів 70 тис.4 роки тому
Learn more theorems in Euclidean geometry and their applications at: brilliant.org/ThinkTwice Please consider supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktwice2580) ► Instagram: thinktwice_ltu (@thinktwice_ltu) Summary: The Fermat point of a triangle ABC is a point P such that the sum of distances PA PB PC is a minimu...
A fun probability puzzle with a neat geometric solution.
Переглядів 53 тис.4 роки тому
Spread the love of math by gifting your friends a Brilliant Premium subscription : brilliant.org/ThinkTwice Please consider supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktwice2580) ► Instagram: thinktwice_ltu (@thinktwice_ltu) Any further questions: ► thinktwiceask@gmail.com Programs used: ► Cinema 4D ► Processing Music...
Constructing a Square of Equal Area to a given Polygon
Переглядів 105 тис.4 роки тому
Explore the world of Euclidean geometry by solving geometry puzzles at: brilliant.org/ThinkTwice Please consider supporting Think Twice on: ► Patreon: patreon.com/Think_twice ► Twitter: thinktwice2580 (@thinktwice2580) ► Instagram: thinktwice_ltu (@thinktwice_ltu) About the video: 1. Pick any polygon 2. Split it up into triangles (While it is trivial to triangulate an...
Alternating series #2 | Visual solution |
Переглядів 33 тис.5 років тому
You can learn more about CuriosityStream at curiositystream.com/thinktwice Support my animations on: www.patreon.com/Think_twice Any further questions: Email: thinktwiceask@gmail.com Twitter: thinktwice2580 Instagram: @thinktwice_ltu thinktwice_... Programs used: - Cinema 4D - Processing Music by: miras2hot
Visual Calculus: Derivative of sin(θ) is cos(θ)
Переглядів 227 тис.5 років тому
Build an understanding behind different concepts of calculus that will help you tackle challenging problems at: brilliant.org/ThinkTwice Proof: Derivative of sin(θ) is cos(θ) Support my animations on: www.patreon.com/Think_twice Any further questions: Email: thinktwiceask@gmail.com Twitter: thinktwice2580 Instagram: @thinktwice_ltu thinktwice_... Programs used: - Cinem...
What is the area under an arc of a cycloid curve?
Переглядів 50 тис.5 років тому
Build an understanding behind different concepts of geometry that will help you tackle challenging problems at: brilliant.org/ThinkTwice Why does the area under a cycloid curve equal to 3 times the area of the circle used to trace out that curve? Support my animations on: www.patreon.com/Think_twice Any further questions: Email: thinktwiceask@gmail.com Twitter: thinktwice2580 Instag...
Napoleon's theorem | Proof |
Переглядів 60 тис.5 років тому
Explore the world of geometry at: brilliant.org/ThinkTwice Napoleon's theorem: "On each side of a triangle, erect an equilateral triangle, lying exterior to the original triangle. Then the segments connecting the centroids of the three equilateral triangles themselves form an equilateral triangle." Support my animations on: www.patreon.com/Think_twice Any further questions or ideas: Email: thin...
Cavalieri's Principle in 3D | Volume of a sphere |
Переглядів 107 тис.5 років тому
To improve your problem solving skills, go to: brilliant.org/ThinkTwice Finding an equation for the volume of a sphere using Cavalieri's Principle ( assuming we already know the equation for the volume of a cone) Support my animations on: www.patreon.com/Think_twice Any further questions or ideas: Email - thinktwiceask@gmail.com Twitter - thinktwice2580 Programs used: - Cinema 4D Mu...
Alternating series #1 | Visual solution |
Переглядів 45 тис.6 років тому
A short animation about a visual solution to an alternating series:) Support my animations on: www.patreon.com/Think_twice Any further questions or ideas: Email - thinktwiceask@gmail.com Twitter - thinktwice2580 Programs used: - Cinema 4D Music: " Gone For Now "- ua-cam.com/video/bkJ-5Pb-514/v-deo.html
Pythagorean theorem | 3 Visual Proofs |
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Pythagorean theorem | 3 Visual Proofs |
Approximating Pi ( Monte Carlo integration ) | animation
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Approximating Pi ( Monte Carlo integration ) | animation
Finding the general formula for nth octagonal number | Visual proof |
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Finding the general formula for nth octagonal number | Visual proof |
Arithmetic mean vs Geometric mean | inequality among means | visual proof
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Arithmetic mean vs Geometric mean | inequality among means | visual proof
Infinite Sums | Geometric Series | Explained Visually
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Infinite Sums | Geometric Series | Explained Visually
Geometry of Binomial Theorem | Visual Representation | 2 examples
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Geometry of Binomial Theorem | Visual Representation | 2 examples
Four squares with constant area | Visual Proof | Squaring the segments |
Переглядів 54 тис.6 років тому
Four squares with constant area | Visual Proof | Squaring the segments |
Geometry: Viviani's theorem | Visualization + Proof |
Переглядів 147 тис.6 років тому
Geometry: Viviani's theorem | Visualization Proof |
Fitting a Cube Through a Copy of Itself | Rupert's Cube |
Переглядів 319 тис.6 років тому
Fitting a Cube Through a Copy of Itself | Rupert's Cube |
Chaos Game | Fractals emerging from chaos | Computer simulation |
Переглядів 332 тис.6 років тому
Chaos Game | Fractals emerging from chaos | Computer simulation |
Unfolding The Dragon | Fractal Curve |
Переглядів 193 тис.6 років тому
Unfolding The Dragon | Fractal Curve |
Double pendulum | Chaos | Butterfly effect | Computer simulation
Переглядів 3,9 млн6 років тому
Double pendulum | Chaos | Butterfly effect | Computer simulation
Cutting a Möbius strip in half (and more) | Animated Topology |
Переглядів 441 тис.6 років тому
Cutting a Möbius strip in half (and more) | Animated Topology |
Area of dodecagon | Beautiful geometry | Visual mathematics
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Area of dodecagon | Beautiful geometry | Visual mathematics
Sum of first n odd numbers | Visual mathematics |
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Sum of first n odd numbers | Visual mathematics |
Your videos are soooooo cool and amazing! BTW, we are the 2 from Taiwan that chatted with you today
Thanks! It was great talking to you, hope you have a nice trip :)
😮
Thanks sir
2:00 -- The two-minute warning
I saw this video in 2020. Now it makes me nostalgic. Yep, nostalgic for 2020.
shit, i came here because of tony stark.
Love this ❤
优雅!
Wurzelkriterium?
Brilliant video!
And what if we cut it by 4
Wow this is just mindblowing!
Nice explaination 👍👍
It's a treat to eyes... Amazing Mathematics 🎉
Always be deeply suspicious of any video which distracts from serious argument by including needless music. This video is an amusing illustration of the misnamed theorem, but no proof to me. However it helped me to spot a simple proof, which depends on the tiling effect shown at the end. There are symmetries which show that bc equals cd, and you can imagine a third red line heading south-east fom c and constructed from a continuation of the tiling. The symmetry will show that the 3 angles at c are equal, so are all 120 degrees. Likewise da = ab, and the angle at a. The rest follows simply from the qualities of the kite abcd.
Get rid of the music.
Why alpha + theta=90
Shinler was here
Those first two moves 💀
Physics can be beautiful🎉
Mag ich sehr gerne zuschauen!!😊
Are there any other examples of this where the sum of powers, is equal to another power of sums? I.e. where the 1^a + 2^a + 3^a + ... + n^a = (1 + 2 + 3 + ... + n)^b?
beautiful ! instant like and subscription!
Nice video, thanks for posting 😊
Лектор доказал эту теорему на занятии по математическому анализу, но не назвал её. Спасибо!
What software did you use to create the animation?
Why the B'AB is measure as 60° ?
The most epic introduction for a laptop ( play from 1:44 at 2x) Edit: Edited timestamp
In minute 1:36, why is (4 x pi x r squared) divided by 2 pi
Great proof
Amazing video; very clear!
Thanks a lot.
i just found ur channel and i neeeeeeeeed u i have trig identities test
please please please upload again
Anyone here from codeforces CodeTon?
"slightly"
fy!
That's literally the best video I have ever seen.
Thank you.
Super nice video!! Your efforts are really appreciated, if you could make a video like these for all geometry theorems in Olympiad it would be pretty cool and I guess would blow up pretty fast. I know it takes a tremendous amount of efforts so thanks!!! (PS how do you animated your videos?)
A great way to explain it by cutting the strips and then twisting them, thanks. I have one for you. If the formula for the surface area of a circle is πr2, should the volume of a sphere be πr3? I would love to see a visual explanation of that.
my hurt heads
The mathematical arm
I love this because it disproves that its chaos and unpredictable the verry fact it is simulated means it is predicted
12 hues of the color wheel. 12 tribes on planet earth. Chaos.
please come back! your vids are amazing please come back
this shit made me feel like i was in a coldplay concert
This is very usefull thank you
for the quadrilaterall, let A,B,C,D in order be the points of the quadrilateral and x the candidate for the "fermat" point. we want to minimize |x-A|+|x-B|+|x-C|+|x-D|. We take the gradient with respect to x and get (x-A)/|x-A|+....+(x-D)/|x-D|=0 for the minimum (assuming it exists). So let a,b,c,d be the vectors that are in the same direction as x-A,...,x-D but with unit length. This means we want a+b+c+d=0, since vector adition is tip to tail this means that we have a quadrilateral with lengths of the same size, ergo they consititue a rombus ergo it is a parallelopiped, so a+c=0, b+d=0. This means that x is between A and C as well as B and D. Meaninf that x is the intersection of AC and BD.
Beautiful vishuvalization