- Видео 68
- Просмотров 21 122
Beauty In Math
Австралия
Добавлен 23 окт 2023
Channel dedicated to share the beauty of #mathematics and explore mathematical concepts using visualizations made with #geogebra and other #programing languages. Made with ❤️ by Juan Carlos. ∞ Thanks for your visit!
More projects in the links below 👇
More projects in the links below 👇
All types of conics, all at once!
A simple yet fascinating geometric method to plot all types of conics.
0:00 Intro
0:28 Parabolas
2:05 Hyperbolas & Ellipses
4:03 All types of conics, all at once
5:15 Challenges
6:19 Enjoy the final animation!
References:
• Boltianskii, V. G. (1964). Envelopes. New York: Macmillan.
• Gutenmacher, V., Vasileiv, N. B. (2004). Lines and Curves: A Practical Geometry Handbook. Boston, MA: Birkhauser.
• Ponce Campuzano, J. C. (2019). Conics as envelopes of families of plane curves. The College of Mathematics Journal. 50-2, 115-122. www.geogebra.org/m/jpzw6zzm
I also recommend you to check @paralogical-dev 's video about envelopes:
ruclips.net/video/fJWnA4j0_ho/видео.htmlfeature=shared
A #desmos version her...
0:00 Intro
0:28 Parabolas
2:05 Hyperbolas & Ellipses
4:03 All types of conics, all at once
5:15 Challenges
6:19 Enjoy the final animation!
References:
• Boltianskii, V. G. (1964). Envelopes. New York: Macmillan.
• Gutenmacher, V., Vasileiv, N. B. (2004). Lines and Curves: A Practical Geometry Handbook. Boston, MA: Birkhauser.
• Ponce Campuzano, J. C. (2019). Conics as envelopes of families of plane curves. The College of Mathematics Journal. 50-2, 115-122. www.geogebra.org/m/jpzw6zzm
I also recommend you to check @paralogical-dev 's video about envelopes:
ruclips.net/video/fJWnA4j0_ho/видео.htmlfeature=shared
A #desmos version her...
Просмотров: 393
Видео
Mysterious Rotating Circles
Просмотров 2,1 тыс.Месяц назад
In this video I show you how to construct in #geogebra a beautiful animation of tangent circles rotating inside each other. I also talked about its relationship with the #geometric #series for #complex #numbers. Note: I re-uploaded this video since I summed polar coordinates by summing the moduli and phases separately, which is not valid. Big 'thank you' to @jursamaj for pointing this out. 🙏 0:...
Golden Ratio: Golden Dragon & Icosahedron
Просмотров 101Месяц назад
Enjoy this short animation of the Golden Dragon & Icosahedron made in #geogebra. • Demo in #geogebra: www.geogebra.org/m/zwfggcvq • The fractal was made using the method from this tutorial: ruclips.net/video/ymIdJX70zjM/видео.html • Check the version with a dodecahedron made in #threejs: ruclips.net/video/QzVxZP6r7xE/видео.html
Golden Ratio: #Fractal Golden Dragon and #Dodecahedron
Просмотров 270Месяц назад
Enjoy this beatiful #fractal animation made with #threejs: www.dynamicmath.xyz/threejs/dodecahedron-fractal/ • A #geogebra version: www.geogebra.org/m/zwfggcvq • Check Bernat Ancochea's construction in #geogebra: www.geogebra.org/m/hausygqw • Another similar #geogebra construction made by Juan Vicente Sánchez: www.geogebra.org/m/s2ratepg • References: larryriddle.agnesscott.org/ifs/heighway/gol...
Domain coloring: Visualizing #complex #functions
Просмотров 1,4 тыс.Месяц назад
What is #domain #coloring? How can we use it to #visualize and study properties of #complex #functions? How can we use it to create abstract #mathematical #art? Note: I re-uploaded this video since there was a missing sign at 5:06. • Multiple online plotting tools in #p5js: www.dynamicmath.xyz/domain-coloring/ • Learn more about Complex Analysis with this interactive textbook: complex-analysis....
Creating a navigation bar to show steps for geometric constructions in #geogebra
Просмотров 2322 месяца назад
Did you know you can use a built-in navigation bar to display the steps of geometric constructions in #geogebra? In this short tutorial I show you how. Enjoy! • Demo: www.geogebra.org/m/s4qcdq3t • GeoGebra online classic: www.geogebra.org/classic • Download Geogebra: geogebra.github.io/docs/reference/en/GeoGebra_Installation/ ❤️ Support the channel on Patreon www.patreon.com/jcponce Or PayPal p...
Rotating Torus Knot | A Dynamic Particle Ballet in 3D Space
Просмотров 1815 месяцев назад
Rotating Torus Knot | A Dynamic Particle Ballet in 3D Space
Hexagonal curves animation | #geogebra suite
Просмотров 1395 месяцев назад
Hexagonal curves animation | #geogebra suite
The Sequence command in #geogebra | Lists of numbers and objects
Просмотров 8366 месяцев назад
The Sequence command in #geogebra | Lists of numbers and objects
Eternal loop: Sphere on Möbius strip
Просмотров 2276 месяцев назад
Eternal loop: Sphere on Möbius strip
Mystery curves | #geogebra suite app
Просмотров 1796 месяцев назад
Mystery curves | #geogebra suite app
Lorenz Attractor | #geogebra suite app
Просмотров 3237 месяцев назад
Lorenz Attractor | #geogebra suite app
Rotating rings | #geogebra suite app
Просмотров 1507 месяцев назад
Rotating rings | #geogebra suite app
How to make a #fractal tree in #geogebra?
Просмотров 1,8 тыс.11 месяцев назад
How to make a #fractal tree in #geogebra?
This plot brought to you by CBS.
Haha! I see what you mean :)
Hello. Do we need to pay money to geogebra to use the geogebra generated images,etc.. in youtube videos?
I don't think so.
Thank you.
How desine this animate?
Excellent explanation. Simply beautiful.
Muy elegante!
Gracias. :)
Excelente
Collapse of the wave function 8 ) almost
Not very familiar with this term. Is it about quantum mechanics? I remember reading something about an algorithm “Wavefunction collapse”.
@@BeautyInMath Sometimes maths is beautiful and of course I am refering to my self when I say sometimes 8 ). What would happen if repeatable scalar structures vs an xy plain canceled out one another and the max distance between tangential circles coresponded to the diameter of internal circles that act as nodal and anti nodal harmonic moduli within the system? I wonder what kind of geometries would be produced? Collapse of the wave function defined as a double measurement maybe... so that if you added a right handed symetry beside this modal and used the diameter of this model to form the radius of a greater circumferance enclosing both circles... allowing for larger circles than shown to extend towards a point of origin between the two systems... and where circles overlap they cancel out like a boundary against infinity where the circle represents an aspect there of and so cannot be produced twice by the same measurement that is to say observer and thus collapse.
Graph: www.desmos.com/calculator/g9asjc6xph Complex Analysis - Conformal mapping complex-analysis.com/content/conformal_mapping.html
Embrace mechanical computing and air gapped simulation, reject absolute connectivity, faith In cybersecurity will soon crash to nothing, not because of cybercapability, but because of how Ai is percieved
great video
@@spidunno Thanks. I hope you try to replicate it and explore more using geogebra or any other program.
"[Quizizz loading screen]" ahh question 🗣️🗣️🗣️🔥🔥🔥
It does look like it :)
❤❤
Cool
Thank! 😃
i put in what you did, but i got a weird infinite star shape
like a bunch of beams
That’s odd. Post you file in the GeoGebra reddit forum. I can check it out and help you there. Also, there are links in the description with the GeoGebra demo. Cheers
@@BeautyInMath maybe its because i am using a newer version?
@@kales901 That should not be a problem. It works for all versions. GGB classic 5, GGB version 6, or even Suite calculator.
@@kales901 geogebra.org/classic?command=n=50;k=2.5;m=3;t=Slider(0,2*pi,0.01,0.3,200);f(x)=(cos(m*x/2)^n--sin(m*x/2)^n)^(1/(k*n));L=Sequence(Curve(j/f(%CE%B8)*cos(%CE%B8),j/f(%CE%B8)*sin(%CE%B8),%CE%B8,j*t,pi--j*t),j,1,10);SetVisibleInView(f,1,false);
"Applied Complex Variables" by John W. Dettman (Dover Publishers) is a great read (The Math Sorcerer has a video on it.): the first part covers the geometry/topology of the complex plane from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. I've used Smith Charts (RF/microwave engineering) for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation. For practical reasons, a typical "Math Methods for Physics & Engineering" course introduces the Cauchy-Riemann Conditions, Conformal Mapping, Contour Integrals and applications of the Residue Theorem, but has to omit a lot interesting details. The Schaum's Outline on "Complex Variables" is a great companion book for more problems/solutions and content.
Thaks for the recomendations. I hope you find the online resource I mentioned in the video also useful. Regards!
Frank Farris deserves a medal! I didn't know who originated this coloring scheme.
I agree! :)
Doc!! Where is "the flux capacitor"??!!
:)
For more info check this: www.dynamicmath.xyz/math2001/chapter-43.html#/3
Siempre nos sorprende con herramientas o conceptos que tenemos delante de los ojos pero no los hemos visto. Muchas gracias por su trabajo.
GeoGebra tiene cientos de herramientas que a veces nos olvidamos que están ahí. :) Saludos.
Gracias por compartir consejos sobre uso de GeoGebra.
Un placer. Saludos! 😃
Very peaceful. Are they all randomly generated? I could imagine an evolutionary version.
Yes they are. This is a classic project made in Processing a while ago. Now it is no longer available and I wanted to understand how it works, so I rewrote in p5.js. In the description you can find all the source code in Processing and p5.js. If you make an evolurionary version, I would love to see it. Cheers!
That’s sooo soouu wonderful! I could look at it for hours and thinking about the creation and all our different own pattern which we made of and we create new ones and the whole material creation is build of these frequence patterns. The Maya network illusion maker…. 💫😮💫😮💫
Hello! I am glad you like it. I made this thanks to Sara Brewer. You can check the online demo made with GeoGebra here: www.geogebra.org/m/kt2wr7wy www.geogebra.org/m/vh8cscqy
God blessing you always
Grow: www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=KC1pKnoqMS4xKV4oMTAqKHQrMSkvMisyKS0x
Spiral: www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=KHoqMykvMiplXih0KnBpKmkqZV4oLTEqYWJzKCh6KjMpLzIpXjIpKQ==
Flower: www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=KCgoMS96XjQgKyAxKSAqICgwK2kgLSAxKSkgLyAoKDEvel40IC0gMSkgKiAoMCtpICsgMSkpKV4oMSt0KjIqaSk=
Check the full video: ruclips.net/video/DKSIXRK6iaM/видео.html
I love this game
A particle life system animation inspired by Terry Soule, aka @programmingchaos8957 • Check out the video with full tutorial: ruclips.net/video/xiUpAeos168/видео.htmlsi=DmRxoykK8O6zWxcl • #threejs interactive demo in 2D: www.dynamicmath.xyz/threejs/particle-life/
Ademas de bonito, acalma la mente.
@@DIGNmatVisual Hola. Me alegra saber que te agrada. Hace un par de días subí otro video con partículas que simulan “vida” y enlaces a interactivos muy relajantes también. Saludos.
Thanks alot
I am glad you liked it! Regards/
How did you do that in particle life
I followed the tutorial from the Video Programming Particle Life. Link in the description.
@@BeautyInMath ok thanks 😀
@@IyadShaikhHi! I just added an extra demo in threejs. Link in the description. Have fun!
@@jcponcemath I was about to say it doesn't work because my dumb 1 IQ brain didn't see the video link
@@IyadShaikh If can’t find the link, just search in RUclips the channel Programming Chaos.
I think there are some passages missed - the program doesn't recognize the command Grow and there is no way to understand how to make the input function recognize it in connection with the newly created tool I guess --- also in the instruction it doesn't specify which language to use - it tells GGB scripting but it seems that for every function there is a precompiled option so copy pasting always gives syntaxis errors - The video misses relevant information as well as the instructions.
The video covers everything you need to do the basic construction. Sorry to hear it does not work on your end. If you want, you can check the links in the description. Some people have been able to replicate this method, as you can see in the Showcase section here www.geogebra.org/m/dwpzpvap#material/gxdekxh4 If that does not work, post your ggb file (link) that does not work on the reddit[dot]com/r/geogebra forum, so I can have a look to it. I am happy to help :)
Eweeweeweweweeweweeweweweweeweweweewewewweewweweewewe
Great!
how to make this in geogebra pls
Hi. It is example 5 here: ruclips.net/video/jZEW_pdRZmM/видео.htmlsi=8WrluY5uF8cyejCZ
I could (and will) watch this for hours
Here is the live demo: www.dynamicmath.xyz/threejs/torus-knot/ Maybe later I will add some music. :) Cheers!
A beautiful animation made with #threejs. Thanks to @robotbobby9 for his amazing tutorial: Learn Three.js: Simple Particle Effects ruclips.net/video/h1UQdbuF204/видео.htmlfeature=shared Music by @TonyAndersonMusic ruclips.net/video/3Tb0NWTVtqE/видео.htmlsi=ILl3Qdxlf0V_HQQH
Cercles et surfaces de révolutions by Jean-Baptiste Etienne www.geogebra.org/m/uydwdbut Thanks for sharing!
Now explaining this to others, is going to be another challenge.
Very cool construction, and great tutorial!
Thanks! I am going to try to make your 12-fold pattern in 6-4-3-4. Such a beautiful design :)
Is there any logic behind your equation writing process ?
To be honest, I found that expression somewhere in the internet a long time ago. But we can analyze what is behind it by studying each term. The main point to create a perdiodic function similar to sine and cosine. The powers with the parameter k, and n help us to create the corners. You can explore this easily in geogebra by defining the sliders and see what happens when you change the parameters n (even numbers from 2 to 50), k (decimal from 1 to 10) and m (decimal number from 1 to 10 with increment of 0.5). I hope this makes sense. Cheers!
@@BeautyInMath thank you , I just very confused when I see this video that how can you create that kind of expression . So I just want to know that how can I do it myself . Go on its great specially in geogebra . 👍👍❤️
Cool
Amazing! I did it! Thank you so much! Very nice tutorial!
If you make a different version, you share it with me in twitter (if you want) @jcponcemath #hexagonalcurves or in a video.
Your videos are incredibly informative. They've demystified many concepts I once found challenging, showing me just how simple they can be.
I am glad you enjoyed it. If you make a different version, hope you can share it in twitter with me. Cheers!
Hello! Did you just need to past this code to get the output? end if yes where?
In the input box of GeoGebra. You can use version 5 or 6 or online. Or copy and paste the link below in your browser: geogebra.org/3d/?command=P=(-4,-4);Q=(4,-4);Zip(Prism(Translate(Dilate(Rotate(Polygon(P,Q,4),6%C2%B0*k),0.9^k),Vector((0,0,0.2*k))),0.2),k,0..60) Also check this part of the video: ruclips.net/video/wQaX-K_8Mjc/видео.htmlsi=o7-QmvMJvAe_rW1g&t=60 I hope this makes sense.
If you want it animated, then use this link: geogebra.org/3d/?command=P=(-4,-4);Q=(4,-4);n=slider(1,60,1,1,200);Zip(Prism(Translate(Dilate(Rotate(Polygon(P,Q,4),6%C2%B0*k),0.9^k),Vector((0,0,0.2*k))),0.2),k,0..n);StartAnimation(n);SetLineThickness(l1,2) Enjoy! 😉
@@BeautyInMath Thank you so much! So beautiful!
Check the full tutorial: ruclips.net/video/8_BLhxjrho0/видео.html
Check the full tutorial: ruclips.net/video/8_BLhxjrho0/видео.html