Pythagorean Theorem
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Google Celebrates Turing’s 100th Birthday
Today, in what would’ve been genius Alan Turing’s centennial birthday, Google is celebrating him with this awesome doodle. Born June 23rd, 1912 - Alan Mathison Turing was a mathematician, logician, computer scientist, and general badass. He’s the father of the concepts of “algorithms” and general computer science. He created the Turing machine, and without that - you definitely wouldn’t be reading this on a computer right now.
Read more about this awesome guy here.
Spiral of Theodorus
First constructed by Theodorus of Cyrene, the spiral (also called the square root spiral, Einstein spiral or Pythagorean spiral) is composed of contiguous right triangles. It is begun with an isosceles right triangle with each leg having a length of 1 - then another right triangle is formed next to it with one leg being the hypotenuse of the prior triangle and the other leg having a length of 1.Thus, each successive nth triangle has side lengths √n and 1, with a hypotenuse of √(n + 1).
Fullerenes and Buckyballs
Despite the seemingly complex name, a fullerene is nothing more than a molecule composed entirely of carbon. That’s all! Fullerenes can come in the shape of a hollow sphere, ellipsoid or tube. When a fullerene is spherical, they are known as buckyballs - and when cylindrical they are called carbon nanotubes or can be affectionately called buckytubes. Fullerenes are similar in structure to graphite, which is composed of stacked graphene sheets of linked hexagonal rings; but they may also contain pentagonal (or sometimes heptagonal) rings.
The first fullerene to be discovered, buckminsterfullerene (C60), was prepared in 1985 by Richard Smalley, Robert Curl, James Heath, Sean O’Brien, and Harold Kroto at Rice University. The name was an homage to Buckminster Fuller, whose geodesic domes it resembles. The structure was also identified some five years earlier by Sumio Iijima, from an electron microscope image, where it formed the core of a “bucky onion.” Fullerenes have since been found to occur in nature. More recently, fullerenes have been detected in outer space. According to astronomer Letizia Stanghellini, “It’s possible that buckyballs from outer space provided seeds for life on Earth.”
The discovery of fullerenes greatly expanded the number of known carbon allotropes, which until recently were limited to graphite, diamond, andamorphous carbon such as soot and charcoal. Buckyballs and buckytubes have been the subject of intense research, both for their unique chemistry and for their technological applications, especially in materials science, electronics, and nanotechnology.
Nikola Tesla (1856-1943)
If one were to choose the most vastly underrated scientist of all time, Tesla would be a fine choice. Although Tesla was a true genius and a complete badass - contemporary society has largely forgotten the man that made modern technology possible.
Most people are at least vaguely familiar with Alternating Current (AC) - it is responsible for running most of our everyday appliances and electrical equipment. This was the work of Tesla. During the so-called ‘War of Currents’ of the late 1880s, while the renowned Thomas Edison was an advocate of Direct Current, Tesla spoke out against him - and was proven correct.
Besides all of this, Tesla also made enormous breakthroughs in the invention of fluorescent lighting. He also invented the super-awesome Tesla coil, shown below. Invented in 1891, version of the Tesla Coil are still used in radios, televisions sets and all sorts of different electric equipment.
Tesla even described the principles of wireless radio - causing one of the harshest science rivalries of all time. Guglielmo Marconi is largely credited with the invention of the radio, but Tesla expressed the idea years beforehand. Marconi used a number of Tesla’s 700 patents for creating the radio. Tesla eventually sued Marconi, and Marconi’s patents were declared invalid in 1935. In a feat of bad luck, Tesla died a few months before the law suit was finalized - and he was never given a penny of compensation.
Newton v. Leibniz - The Calculus Controversy
In Latin, the word ‘calculus’ means ‘pebble,’ meaning that small stones were used to calculate things. Calculus is essentially the study of change, and the pebbles represent small, gradual changes that can produce impressive results. The origin of calculus is not the work of a single man, not even the work of the two men pictured above - but like most major discoveries, a gradual build of overlapping discoveries, something very similar to calculus itself. The question over the creation of the branch of mathematics has become one of the fiercest rivalries in modern history - that between Isaac Newton and Gottfried Leibniz.
In 1666 (and perhaps earlier), when Newton was 23 - he had begun work on what he called “the method of fluxions and fluents,” effectively what we know as calculus. Newton’s discovery of calculus was mainly a result of practical use - he needed a method to solve problems in physics and geometry, and calculus was what resulted. On the other hand, Leibniz had become fascinated by the tangent line problem and began to study calculus around 1675.
The ideas of the two men were similar, although it is unlikely that either of them knew the specifics of the other’s work. The two men spoke in letters often, and discussed mathematics - and although the Royal Society found Leibniz effectively guilty of plagiarism later, this was not likely the case. Both men came to similar discoveries in different ways - Leibniz came to integration first, while Newton began his work with derivatives.
Although Newton discovered the principles of calculus first - he did not publish them until many years after Leibniz did. Leibniz published his first paper employing calculus in 1684, but Newton did not publish his fluxion notation form of calculus until 1693, and a complete version was not available until 1704! Nonetheless, Newton still came to the discovery first - and although both men are officially credited, Newton is the one that most people remember.
However, Newton doesn’t deserve all the credit here. The famous dy/dx notation that calculus students have come to love and hate was developed by Leibniz. Although Newton may have come to the discovery first, Leibniz attacked the problems with far better notation - and we have naturally adopted it. Instead of Leibniz’s dx/dt (shown below) notation for derivatives, Newton preferred ‘dot’ notation:
However, this dot notation can become confusing, especially when used for higher order derivatives, so it has been generally dismissed - except for hardcore Newton fanatics who insist on using his notation. Newton did not even have a standard notation for integration, but frequently switched; but Leibniz used the recognizable integration symbol:
This has developed into a fantastic controversy over the years - and has become as much of a moral question as it is scientific. Many Leibniz advocates belief that Newton doesn’t deserve full credit because he didn’t publish his findings first - while many others believe that Newton came to the discovery first, so the credit is his. Personally, I have to place myself on the side of Newton - although Leibniz’s notation is wonderful, Newton discovered the principles first.
Which side are you on?
