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Isis Kearney

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I made this video and have started a channel. Would be great if people could watch it and subscribe. Feedback is always welcome.
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Beautiful Fractal gears.
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Jorge Cruz's profile photoDagmar Bornemann's profile photoAda Gil Ibáñez's profile photoSalih DEMİRTAŞ's profile photo
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F Homan
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It's a combination of 2 of my favorite things: clockwork and fractals!
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Wayne Linn

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Richard Krajewski's profile photoJohn Grogan's profile photoMiljana Janjic's profile photobrigid edwards's profile photo
3 comments
 
And yet, wau remains the loneliest number.
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Jean DAVID

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Parallelogram squares - Solution 

Visual solution here : http://tube.geogebra.org/student/m927069
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tekad matulatan's profile photoFlorence B's profile photoOlivier C.'s profile photoKrishna Annangi (Krish)'s profile photo
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Elegant
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Jean DAVID

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Parallelogram squares
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Torolf Sauermann

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reaction diffusion bunny stanford "rendering blender + cycles"
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Matheredix Einstein

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Who knew you could calculate pi just by chucking some hot dogs? This is called the "Buffon's Needle Problem". Check out this video for some other cool facts you might not know about the irrational number.
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Aldrin Mathias's profile photoThe Awesomely, Awesome Bird's profile photoTherese Horley (My Maths House)'s profile photorosario casamayor's profile photo
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The unit circle was what I was thinking of, because I had just left class after an exam and it was pretty trig heavy hehe for 360° the arc length is 2(pi) rad. Also, the formula for the circumfrence for a circle is P=2(pi)r, so if you plug a 1 in.... Lol

The person wrote earlier that he meant to write "diameter of 1" in the video though, which is true. He just made a typo is all.
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Jean DAVID

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Bisector of right angle and square of hypotenuse
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Snail Erato's profile photoIlan Amity's profile photo
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Let G be the center of ACEF
G is on the circle that encircle ABC (AC is diameter)
G is also on BD (BD is a bisector of B)
Hence the blue area and the green area are equal 
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The Pythagorean experiment.
Simple, yet effective.
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rosario casamayor's profile photoWinfried Klum's profile photoFabian Hernandez's profile photoBrian Beck's profile photo
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That is a brilliant demonstration.
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Jean DAVID

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Solution - Bisector of right angle and square of hypotenuse
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Short cut : Let's name a point of red line that cut the line AC and EF is G and D. Compare angles :
∠AGD = ∠GDE
∠CGD = ∠GDF
∠A = ∠F = ∠C = ∠E = 90°
⇒  A (AGDF) = A (CGDE) 
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Khalid Kyle

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Magical of Math :)
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To be seen bySwathi
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Jean DAVID

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Calculus 

- from FB Physics Page
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Hmm, I heard Mark Price used a similar approach at the line for his FTs back in his days.   What's the formula for a "frozen rope," anyone know? 
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Yiannis Galidakis

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phi(n) and GCD(m,n)

Attempts are often made to graphically display the distribution of primes. Before one tries such attempts, it is educating to look first at the graph of Euler's Totient function phi(n) versus n.

http://en.wikipedia.org/wiki/Euler%27s_totient_function

The totient function doesn't only show the distribution of primes, but also the distribution of all the composites as a density. In the graph of phi(n) vs n, the primes are seated at the top, belonging to the line x-1, since phi(p)=p-1 for primes.

Trend  lines with increased density appear on the graph. They are the densities of composites of specific forms. For example, the line x/2 hosts composites of the form 2^n. The lines  x/3 and 2x/3 host composites divisble by 3, etc. Highly composite numbers tend to congregate towards the bottom and composites with large prime factors tend to congregate near the top (below the x-1 line).

Now look at the graph of execution speed performance of the GCD(m,n) algorithm. In this graph, black denotes highest speeds (fast completion) and white slowest, for all positive m,n with 1<=m,n<=200.

http://en.wikipedia.org/wiki/Euclidean_algorithm

Finally check the graphs of the totient and GCD performance combined in Photoshop. You can obviously ignore the symmetric part above the line x, since GCD(m,n)=GCD(n,m)

Can you express the evident connection as a theorem? :-)

[On this post the combined image shows first. The graphs of phi(n) and that of the GCD performance are shown separately in images 2 and 3]
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Thx, I'll give it a whirl in the next few days.
d
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Daniel Lamb

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If you have not tried Fyre yet, you should! Images are based on the Peter de Jong map equations:

x' = sin(a * y) - cos(b * x)
y' = sin(c * x) - cos(d * y)

http://fyre.navi.cx
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Scott Ellis's profile photoOlivier de Broqueville's profile photo
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400 sequences decomposed into weight × level + jump

#math   #numbers   #OEIS   #sequences   #primenumbers   #threejs  
Decomposition into weight * level + jump - 3D graphs (WebGL three.js) - 2D graphs - First 500 terms - This decomposition is a generalization of the sieve of Eratosthenes - 400 sequences decomposed (natural numbers, prime numbers, triangular numbers, composite...) - Rémi Eismann
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Isaac Calder

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here is a concave dodecahedron, which is a remarkable solid in its own right.. [V= 20, F=12, E= 30]; symmetry: Th (tetrahedral complete w. horiz. reflection)
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The Awesomely, Awesome Bird's profile photoTherese Horley (My Maths House)'s profile photoAyush Arvind's profile photoXin Jiang's profile photo
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I thank you very much, madam, for your very kind words of appreciation. I take the opportunity to wish you all the very best in your life.
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Isaac Calder

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the polyhedron at left (we shall see it is nothing but a regular dodecahedron) was obtained taking an ordinary cube and then putting on each of its 6 faces (as an augment) a roof that consists of 2 isosceles trapezoids (in pink & green) with common minor basis plus 2 isosceles triangles (in yellow & blue) to complete the roof (the bases of the roofs are squares congruent to the square faces of the cube); the roofs were constructed so that each of its trapezoids together with a triangle of the nearest roof make a regular pentagon and so we get the primitive cube covered by 6 roofs making NOT 4*6=24 faces but only 4*6/2=12 faces (pentagons) of the regular dodecahedron
the same thing is done in the next gif (at right) , except that the roofs are not augmented outwards as before but excavated inwards making now a concave dodecahedron as a result; in the figure there are 12 triangles that don't make part of the concave dodecahedron but are used only for technical reasons as we will see when we combine both kinds of dodecahedra (convex= ordinary regular & concave) in next posts
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+Mark Steinberger I am posting in another place in this community the concave dodecahedron free of 'parasitic' triangles (q.v.)
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Abhishek Singh Rawat

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The greatest equations that changed the world, forever.
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+Christian Hujer Well, I think we will never agree. Europe economy affects the world, not like the USA but still, it can not be ignored, it's an important component of the world economy.
What's more, the Black–Scholes theory shows the power of mathematics in describing fields that are not considered as standard science, and here lays its importance. It's not a question of the EU or Japan or whatever, it's the predictive power of a mathematical theory in a field that seems chaotic. 
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Khalid Kyle

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Looks awesome! Hope it will be sell soon :)
 
Ruler that automatically measures angles and etc.
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Rakesh Bhagga's profile photovikas v's profile photoTyler Quan's profile photoOm prakash prajapat's profile photo
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wow,that's awesome
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