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Xaroula Kosta

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“The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.”

~ D'Arcy Wentworth Thompson
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Eden G

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Good morning everyone.😊🌹☕
Axis of Oscillation (b-side)
Found this on tumblr
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Martin Dillon's profile photo
 
Better yet, program your own illusion.
https://scratch.mit.edu/projects/12248315/
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Eric Pouhier

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+Marius Buliga​ works are very inspirational!
 
Fractal explosion. Like in the last post [1], I used the test scripts from the chemlambda repository in order to produce a simultaneous creation and duplication of the fractal like molecule representing 4^4. You can make the same by repeating the procedure described in [1], but for the mol file 4_exp_4_foe.mol. If you compare it with it's brother 4_exp_4.mol, then you'll see that it's shorter :) How come?

These mol files are part of the chemlambda mol files library [2] which has hundreds of molecules to play with.

Incidentally, I've opened a project [3] at ResearchGate about molecular computers, if interested to connect through that walled garden then please do it.

[1] Fractal out of the box
https://plus.google.com/+MariusBuliga/posts/jjamPTNitar

[2] Library of chemlambda molecules
https://github.com/chorasimilarity/chemlambda-gui/tree/gh-pages/dynamic/mol

[3] Molecular computers, graph rewrite systems and decentralized computing
https://www.researchgate.net/project/Molecular-computers-graph-rewrite-systems-and-decentralized-computing
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Yuriy Fazylov (Yuriyology)'s profile photoDavid Kotschessa's profile photo
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Wow. It looks very organic. A sort of controlled biological chaos, like a heartbeat. 
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LEARN EASILY

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This video explains how to solve integration by method of substitution in calculus. Useful for class 12 students & IIT JEE examination.
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RAMA SUBBA REDDY's profile photo
 
What is integral of square root of sinx by x
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Banjar Agung

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Like n subscribe ya... terima kasih
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Jean DAVID

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Area of a sphere
by Sigmond Endre "Magic pencil"
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Matej Kohut's profile photoRene Grothmann's profile photo
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I like the following way: The ancient Greeks figured out the volume of the half sphere by comparing it to a cylinder minus a cone. The surface is the derivative of the volume with respect to the radius: dV/dh = dO is quite natural if you explain it.
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Isaac Calder

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... and this is the 2nd... [2227=17*131]
please be happy & enjoy being alive!..
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Math

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Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under the condition that neither tested component is defective.
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that Guy's profile photoJosue Guzman's profile photo
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Bayes theorem. 
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LEARN EASILY

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This video explains how to solve the integration by method of substitution in calculus for class 12 students.
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Kevin Clift

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William Hamilton The Music Video
via +Joel David Hamkins 

+Evelyn Lamb reports, here, on a fun and educational music video featuring Irish Mathematician and Physicist William Hamilton, famous in Physics circles for his Hamiltonians, and in Pure Maths for his Quaternions.

A few years ago, a hip-hop musical about the founder of our financial system seemed laughable. But creative genius Lin-Manuel Miranda showed us all it could be a mega-hit. And the parodies, oh, the parodies! Batlexander Manilton, I am not throwing away my Spock, William Henry Harrison, Jeb! An American Disappointment. The list goes on.

Who else deserves this treatment? Obviously, the great Irish mathematician and physicist William Rowan Hamilton, whose name has exactly the same number of syllables and emphasis pattern as Alexander Hamilton. It writes itself!

More here (article): http://goo.gl/i7U74f

Video (YT ~5mins.): https://goo.gl/t7GqIY

All this may may make you anxious to learn more about Hamilton and his exploits.

William Rowan Hamilton's father, Archibald Hamilton, did not have time to teach William as he was often away in England pursuing legal business. Archibald Hamilton had not had a university education and it is thought that Hamilton's genius came from his mother, Sarah Hutton. By the age of five, William had already learned Latin, Greek, and Hebrew. He was taught these subjects by his uncle, the Rev James Hamilton, who William lived with in Trim for many years. James was a fine teacher.

William soon mastered additional languages but a turning point came in his life at the age of 12 when he met the American Zerah Colburn. Colburn could perform amazing mental arithmetical feats and Hamilton joined in competitions of arithmetical ability with him. It appears that losing to Colburn sparked Hamilton's interest in mathematics.

More here (bio): http://goo.gl/h1psKD

It is remarkable that, while he possessed such powers of calculation, and was almost prodigal in the exercise of them, he was to the last degree solicitous about the metaphysics of every subject on which he undertook to write. We have seen a decisive instance of this tendency of his mind ill his treatment of algebra considered as the science of pure time. So, again, in laying the foundation of his Calculus of Quaternions, we see him labouring to secure its stability by the most careful regard to the primary conceptions of time and space. Students of his lectures on Quaternions have sometimes complained that he has claimed from them too much attention to the metaphysics of the subject, and has stopped them in their career of building up, in order that they might contemplate afresh the plan of the structure. But this was in accordance with his views regarding the ascending scale of the subjects of human thought. To religion he gave the highest place, and this not as a formality; for his was a deeply reverential spirit. He assigned the next to metaphysics. To them he subordinated mathematics and poetry, and assigned the lowest place to physics and general literature. His studies in the department of metaphysics were extensive. After a thoughtful examination of Berkeley's writings, he professed himself a disciple of that philosopher, "with most cordial and delighted submission;" not, indeed, assenting to every separate argument, but embracing his grand results; and in this attachment to Berkeley's theory we have reason to know that he was confirmed by his converse with Faraday, who, in his own region of investigation, had been led to the conclusion that forces, rather than material particles, were the ultimate objects of physical inquiry. His acquaintance with the German language enabled him to master the works of Kant. In the reasonings of that philosopher he was the more ready to concur, as his own previous inquiries had already conducted him to several of Kant's views respecting the in tuitions of time and space.

Even more here (address): http://goo.gl/heeJbP

Sir William Rowan Hamilton (midnight, 3–4 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In pure mathematics, he is best known as the inventor of quaternions.

William Rowan Hamilton (Wikip): https://goo.gl/9Z7sb5

Image: https://goo.gl/A49lvc
Broom or Brougham Bridge
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Isaac Calder

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the polychoron (actually a 10-choron or 10-cell) of which you can see the development or net in 3D, has the following cells:
2C + 2H + 2A + 4B
C is a cube of edge 2
A is an offcenter pyramid type A with square base & lateral faces (all right trigs):
2 x (2,2,2sqrt(2)) + 2 x (2,2sqrt(2),2sqrt(3))
B is an offcenter pyramid type B with sq. base & lat. faces (all right trigs):
2 x (2,2sqrt(2),2sqrt(3)) + 2 x (2,2sqrt(3),4)
it is well known that 3 off-center pyramids type A glued around an edge of length 2sqrt(3) make a cube (C)
I use the symbol H (heptahedron) to mean the non-convex solid made of 2 glued A-pyramids with a 2*sqrt(3) common edge, so
2C + 2H + 2A + 4B = 2 cubes, 2 heptahedra, 2 A-pyramids, 4 B-pyramids (pay attention 1H + 1A = 1C)

now, the decachoron spoken of above is a non-convex half-tesseract (or a half 4-hypercube) & 2 equal such hypersolids glued appropriately in 4D make a tesseract (or 8-cell or 4D-hypercube)

pay attention that a gluing in 4D between 2 identical cells make those disappear inside the 4th dimension (just as when you in 3D have 2 ordinary square pyramids & glue them through their bases, the result is a solid with 8 trig. faces,i.e. the 2 bases were glued out inside the solid); in the present case the 2 hypersolids are such that they can be glued simultaneously through 4 B-pyramids so that there disappear 8 B-pyramids at the same time, inside the final tesseract.
in short
2C +2H +2A +4B +
2C +2A +2H +4B = 2C +2C =4C; 2H+ 2A =2C; 2A+ 2H =2C & 4B+ 4B= nil (glued out inside the 4D-hypercube)

[it is a bit long, so please read it again if needed]
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Isaac Calder

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here you have a handsome non-convex octatetracontahedron (48 trig faces) of face vector [V=26, F=48, E=72]; the symmetry of the 'animal' is octahedral complete with horiz. reflection [Oh]
please be well, you all.
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Matt McIrvin's profile photoIsaac Calder's profile photo
5 comments
 
you are correct!, though I have obtained the 'animal' through some other process; thank you for writing that! cheers!
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LEARN EASILY

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This video explains how to solve some typical examples on trigonometric limits.
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nytom4info's profile photoAmy Queque's profile photo
2 comments
 
When i was in high school, we used to solve trigonometric functions. Its really hard to solved this but if you will know the formula its not that too hard.
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Yohan Bream

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Hi. If you need basic math formulas at your fingertips, here you can find a simple lightweight android app. All formulas are scalable without pixelation (vector graphics) and presented in a nice LaTeX-like style :))).
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У додатку Math Formulas Vec наведено основні математичні формули. Для представлення контенту використано векторну графіку (SVG), оскільки такий підхід дозволяє збільшувати зображення без втрати якості (без пікселізації).Базові розділи: - Алгебра (рівняння, комплексні числа, степені, логарифми і т.д.) - Геометрія (трикутник, чотирикутник, коло, об'ємні тіла і т.д.) - Тригонометрія (основні тотожності, обернені функції і т.д.) - Аналіз (границі, по...
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Math

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Mid point of Normal x-intercept and Tangent y-intercept traces out another curve as original point moves round an ellipse.
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Bruce Mincks's profile photo
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By that analysis, however, the {abc} right triangle form is based on a diameter which extends iinto a Z=xy axis. The latus rectus is the diagonal. Thus the number "4" among your terms really affects the 4ac = (x + y)^2 - (x + y)^2 correspondence between "double points" on an ellipse and a hyperbola with referenecne to the b^2 = 4ac discrimant in the (positive or negative) roots of polynomial equations.

At half the sine or secant (depending on your definitions) then "b" is a harmonic mean between units of "c" and this hypotenuse which expresses the deviations of Z from the origins of (2a) rather than the metric of origins for {x, y}. We have perpendicular axes at Z = xy and similar axes where C=ab moves along the curve.

https://plus.google.com/108657187448883149300/posts/iN6kejfPEFQ


A parabola is not a central conic. You can imagine its vertex spinning into a circle on the surface of a sphere; it doesn't emerge from any spherical center. It figures into "equals" dynamically rather than "more or less" in magnitudes of distance or time.

Even if you don't subscribe to Newton's mechanical system by favoring relativity among indiscriminate roots, you still have to admire his breaktrhoughs with conic sections at the start of his Mathematical Principles.
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Banjar Agung

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Like dan subscribe ya. Terima kasih
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LEARN EASILY

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This video explains some typical examples on slope of tangent & normal to the curve in applications of derivatives.
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Meni Porat's profile photoLEARN EASILY's profile photo
2 comments
 
+Meni Porat Ok. Thanks ...
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Isaac Calder

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there are only 2 known integer heptagons in general position;
this is the 1st...
[2227=17*131]
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Jean DAVID

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Geometric series
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Torolf Sauermann

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Endrass octic - version

A gif animation showing the action of the rotation in zw plane.

Licence for this GIF animaion: Creative commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) (https://creativecommons.org/licenses/by-sa/3.0/deed.en)
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