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Science and Math
Science and Math World

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

[#Einsteinsmama]

Koch Snowflake: Finite area, Infinite perimeter.The Koch Snowflake has finite area but infinite perimeterâŚ yeah that happens with fractals. This abstract curve requires an infinite process (depicted in the gif) to construct and is an example of a

fractalâa 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.Â Iâll 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 âfather of fractalsâ) 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

âthe geometry of natureâ. 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 firstStar Warsmovies 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.

The 3 Greatest Minds of All TimeItalianÂ polymathÂ 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 ofÂ palaeontology,Â iconology, and architecture, and is widely considered one of the greatest painters of all time. Sometimes credited with the inventions of theÂ parachute,Â helicopterÂ andÂ tank,Â he epitomised theÂ Renaissance humanistÂ ideal. Today, Leonardo is widely considered one of the most diversely talented individuals ever to have lived.

2. Isaac NewtonEnglish physicist and mathematician (described in his own day as a ânatural philosopherâ) who is widely recognised as one of the most influential scientists of all time and a key figure in theÂ scientific revolution. His book âMathematical Principles of Natural Philosophy,â first published in 1687, laid the foundations forÂ classical mechanics. Newton made seminal contributions toÂ optics, and he shares credit withÂ Gottfried Wilhelm LeibnizÂ for the development ofÂ calculus. Newton’sÂ PrincipiaÂ formulated theÂ laws of motionÂ andÂ universal gravitation, which dominated scientistsâ view of the physical universe for the next three centuries. Newtonâs work removed the last doubts about the validity of the heliocentric model of the Solar System. Newton built the first practicalÂ reflecting telescopeÂ and developed aÂ theory of colour based on the observation that aÂ prism decomposes white light into the many colours of theÂ visible spectrum. He formulated anÂ empirical law of cooling, studied theÂ speed of sound, and introduced the notion of aÂ Newtonian fluid. In addition to his work on calculus, as a mathematician Newton contributed to the study ofÂ power series, generalised the binomial theorem to non-integer exponents, developed aÂ methodÂ for approximating the roots of a function, and classified most of theÂ cubic plane curves. Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study ofÂ biblical chronology andÂ alchemy, but most of his work in those areas remained unpublished until long after his death.

1. Nikola TeslaSerbo-Croation/American inventor, discoverer, electrical engineer, mechanical engineer, theoretical and experimental physicist, mathematician, futurist and humanitarian. Tesla was a hyperpolyglot who could speak eight languagesÂ 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 Goetheâs âFaust,âÂ NjegoĹĄâ âThe Mountain Wreath,âÂ Danteâs âDivine Comedy,â Shakespeareâs âHamlet,âÂ Byronâs âChilde Haroldâs Pilgrimage,â andÂ Pushkinâs âEugene Onegin.â 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 modernÂ alternating current (AC)Â electricity supplyÂ system that we still use today. Tesla was the first to invent and patent a commutatorlessÂ 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.Â 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 âWorld System,â 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.