### Isis Kearney

Videos/Pictures -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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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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F Homan

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It's a combination of 2 of my favorite things: clockwork and fractals!

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And yet, wau remains the loneliest number.

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reaction diffusion bunny stanford "rendering blender + cycles"

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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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Jimmy Amato

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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.

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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Bisector of right angle and square of hypotenuse

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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

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.

Simple, yet effective.

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That is a brilliant demonstration.

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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)

∠AGD = ∠GDE

∠CGD = ∠GDF

∠A = ∠F = ∠C = ∠E = 90°

⇒ A (AGDF) = A (CGDE)

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To be seen bySwathi

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Calculus

- from FB Physics Page

- 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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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]

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.

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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

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

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

http://fyre.navi.cx

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#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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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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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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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

the same thing is done in the next

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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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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.

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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Looks awesome! Hope it will be sell soon :)

Ruler that automatically measures angles and etc.

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wow,that's awesome

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