Category: mathematics

hahahahahahahahahahahahahahahahahahahahahahaha…

hahahahahahahahahahahahahahahahahahahahahahahahaha 😂😂😂😂

Quick mafs

Quick mafs

Merry Christmas in Mathematics

Merry Christmas in Mathematics

asapscience: Mathematicians finally cracked L…

asapscience:

Mathematicians finally cracked László Fejes Tóth’s zone conjecture, a 44-year-old geometry problem! Learn about it here: http://bit.ly/2Cxqp0C

[#Einsteinsmama]

mathblab: Koch Snowflake: Finite area, Infinit…

mathblab:

Koch Snowflake: Finite area, Infinite perimeter.

The Koch Snowflake has finite area but infinite perimeter… yeah that happens with fractals. This abstract curve requires an infinite process (depicted in the gif) to construct and is an example of a fractal–a mathematical set (usually a curve or geometric figure) which exhibits a repeating pattern that displays at every scale. (More about fractals here https://en.wikipedia.org/wiki/Fractal)

But How? It seems clear that the area would be finite since the figure encloses a finite amount of space. To grasp why the Koch Snowflake has infinite perimeter, notice how as the iterations progress, the edges become more and more intricate. Now imagine trying to draw the edges with a pen. Since the construction of the snowflake continues indefinitely, the edges become infinitely intricate and you could never finish detailing these intricacies with your pen (that is the intuitive argument at least. I’ll leave the precise calculations up to you).

Fractals may seem so abstract and impractical but they actually have many useful real-world applications. For example, Benoit Mandelbrot (considered the “father of fractals”) found that stock market prices could be modeled with a factual curve. Check the wiki page for a long and diverse list of applications.

Fractal geometry may seem more abstract than traditional geometry but Mandelbrot argues that fractals are “the geometry of nature”. Objects in nature have random irregularities and are seemingly infinite in their intricacies. Attempting to incorporate this in drawings or animations is extremely difficult. Movie special effects and CGI often use fractals to make objects appear more natural looking. Since fractals can be made with mathematical formulae they are easy to generate with a computer. The first Star Wars movies were renowned for their special effects and were some of the first to use fractals to generate life-like explosions and landscapes of other worlds.

Photo

Via Extra Ordinary

Via Extra Ordinary

drnikolatesla: The 3 Greatest Minds of All Time 3. Leonardo Da…

drnikolatesla:

The 3 Greatest Minds of All Time

3. Leonardo Da Vinci

Italian polymath whose areas of interest included invention, painting, sculpting, architecture, science, music, mathematics, engineering, literature, anatomy, geology, astronomy, botany, writing, history, and cartography. He has been variously called the father of palaeontology, iconology, and architecture, and is widely considered one of the greatest painters of all time. Sometimes credited with the inventions of the parachute, helicopter and tank, he epitomised the Renaissance humanist ideal. Today, Leonardo is widely considered one of the most diversely talented individuals ever to have lived.

2. Isaac Newton

English physicist and mathematician (described in his own day as a “natural philosopher”) who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book “Mathematical Principles of Natural Philosophy,” first published in 1687, laid the foundations for classical mechanics. Newton made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for the development of calculus. Newton’s Principia formulated the laws of motion and universal gravitation, which dominated scientists’ view of the physical universe for the next three centuries. Newton’s work removed the last doubts about the validity of the heliocentric model of the Solar System. Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes white light into the many colours of the visible spectrum. He formulated an empirical law of cooling, studied the speed of sound, and introduced the notion of a Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study of power series, generalised the binomial theorem to non-integer exponents, developed a method for approximating the roots of a function, and classified most of the cubic plane curves. Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study of biblical chronology and alchemy, but most of his work in those areas remained unpublished until long after his death.

1. Nikola Tesla

Serbo-Croation/American inventor, discoverer, electrical engineer, mechanical engineer, theoretical and experimental physicist, mathematician, futurist and humanitarian. Tesla was a hyperpolyglot who could speak eight languages including: Serbo-Croatian, English, Czech, French, German, Hungarian, Italian, and Latin. He claimed to have had a three-dimensional memory and thought process that tormented him in his youth, but later aided him with building his inventions in his own mind without wasting any physical energy. He was known to be able to recite by heart full books, mathematical formulas and poetry such as Goethe’s “Faust,” Njegoš’ “The Mountain Wreath,” Dante’s “Divine Comedy,” Shakespeare’s “Hamlet,” Byron’s “Childe Harold’s Pilgrimage,” and Pushkin’s “Eugene Onegin.” Tesla has more original inventions to his credit than any other man in history. He has been accounted for 278 patents in 26 different countries. He is best known for his contributions to the design of the modern alternating current (AC) electricity supply system that we still use today. Tesla was the first to invent and patent a commutatorless alternating current induction motor that led to an AC/DC war with Thomas Edison. All electrical machinery using or generating alternating current is due to Tesla, without which our our electrified power lines, and our subways would be farless advanced. The Tesla Induction Motor, the Tesla Rotary Converter, the Tesla Phase System of Power Transmission, the Tesla Steam and Gas Turbine, the Tesla Coil ( used for radio technology), and the Oscillation Transformer are perhaps his better known inventions. In his labs he conducted a range of experiments with mechanical oscillators/generators, electrical discharge tubes, and early X-ray imaging. He is also the father of remote control, building a wireless controlled boat exhibited in 1898. Although not recognized for, he was the first to discovery the electron, radioactivity, cosmic rays, terrestrial resonance, stationary waves (standing waves), and the first to invent fluorescent light bulbs. He first demonstrated wireless energy/power by lighting his phosphorescent light bulbs wirelessly in a demonstration given before the Franklin Institute in Philadelphia,1893. He also theorized a particle beam to be used for defense in war, and also to produce an artificial Aurora Borealis to light the night skies, and a particle beam to be used for defense in war. He intended to unify all his innovations into one big machine known as his “World System,” but lacked the investments and funds to finish his work on a large scale. His failure to accomplish his goals left him with a distorted persona of a mad scientist, and a dreamer whose imagination created an unrealistic hope for the future. Tesla would eventually die penniless and alone in his New York apartment, but like the two greats above, he lives on through all his inventions and contributions to this world that last until the end of man.

Ahead of their time!

The 3 Greatest Minds of All Time 3. Leonardo Da Vinci2. Isaac…

The 3 Greatest Minds of All Time

3. Leonardo Da Vinci

2. Isaac Newton

1. Nikola Tesla

drnikolatesla: Nikola Tesla was asked to select his choice of…

drnikolatesla:

Nikola Tesla was asked to select his choice of the greatest modern and future wonders, but the electrical wizard refused to accept the popular notion of what is wonderful. His reply led to an onslaught on scientists who have abandoned “cause and effect” and who take the position that there are accidents in nature and that anything might happen.

“To the popular mind, any manifestation resulting from any cause will appear wonderful if there is no perceptible connection between cause and effect. For instance, through the means of wireless telephone speech is carried to opposite points of the globe. To the vast majority this must appear miraculous. To the expert who is familiar with the apparatus and sees it in his mind’s eye the result is obvious. It is exactly as though visible means existed to which the impetus is transmitted.

“As I revolve in my mind the thoughts in answer to your question I find the most wonderful thing is the utter aberration of the scientific mind during the last twenty five years. In that time the relativity theory [Albert Einstein], the electron theory [J. J. Thomson], the quantum theory [Max Planck, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Arthur Compton, Paul Dirac, Wolfgang Pauli], the theory of radioactivity [Marie Curie] and others have been worked out and developed to an amazing degree. And yet probably not less than 90 per cent of what is thought today to be demonstrable scientific truth is nothing but unrealizable dreams.

“What is ‘thought’ in relativity, for example, is not science, but some kind of metaphysics based on abstract mathematical principles and conceptions which will be forever incomprehensible to beings like ourselves whose whole knowledge is derived from a three-dimensional world.

“The idea of the atom being formed of electrons and protons which go whirling round each other like a miniature sun and planets is an invention of the imagination, and has no relation to the real nature of matter.

“Virtually all progress has been achieved by physicists, discoverers and inventors; in short, devotees of the science which Newton and his disciples have been and are propounding.

“Personally, it is only efforts in this direction which have claimed my energies. Similar remarks might be made with respect to other modern developments of thought. Take, for example, the electron theory. Perhaps no other has given rise to so many erroneous ideas and chimerical hopes. Everybody speaks of electrons as something entirely definite and real. Still, the fact is that nobody has isolated it and nobody has measured its charge. Nor does anybody know what it really is.

“In order to explain the observed phenomena, atomic structures have been imagined [Quantum Mechanics], none of which can possibly exist. But the worst illusion to which modern thought has led is the idea of ‘indeterminacy’ [ex. Uncertainty Principle: W. Heisenberg, E. Schrödinger]. To make this clear, I may remark that heretofore we have in positive science assumed that every effect is the result of a preceding cause.

“As far as I am concerned, I can say that after years of concentrated thought and investigation there is no truth in nature of which I would be more fully convinced. But the new theories of ‘indeterminacy’ state this is not true, that an effect cannot be predicted in advance.

“If two planets collide at certain time and certain place, this is to the student of positive science an inevitable result of preceding interactions between the bodies; and if our knowledge would be adequate, we would be able to foretell the event accurately.

“But in the spirit of the new theories this would simply be an accident. ‘Indeterminacy’ introduces into the world of inert matter a principle which might virtually be compared with the universal illusion of free will.

“Of course, there is no such thing. In years of experimenting I have found that every thought I conceive, every act I perform, is the result of external impressions on my senses.

“It is only because the vast majority of human being are not observant sufficiently that they live in the illusion of perfect choice and freedom in their thoughts and actions. And if this holds true even in the most complex and involved manifestations of human life, it holds true with the same force in all the world of matter.”

–Nikola Tesla

“Great Scientific Discovery Impends.“ The Sunday Star, Washington D.C., May 17, 1931.