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Posts Tagged ‘algebra

“Oh, there you are Peter”*…

 

The missing links between galaxies have finally been found. This is the first detection of the roughly half of the normal matter in our universe – protons, neutrons and electrons – unaccounted for by previous observations of stars, galaxies and other bright objects in space.

You have probably heard about the hunt for dark matter, a mysterious substance thought to permeate the universe, the effects of which we can see through its gravitational pull. But our models of the universe also say there should be about twice as much ordinary matter out there, compared with what we have observed so far.

Two separate teams found the missing matter – made of particles called baryons rather than dark matter – linking galaxies together through filaments of hot, diffuse gas

Get galactic at: “Half the universe’s missing matter has just been finally found.”

* meme

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As we heed E.M. Forster, we might recall that it was on this date in 1843 that Sir William Rowan Hamilton conceived the theory of quaternions.  A physicist, astronomer, and mathematician who made important contributions to classical mechanics, optics, and algebra, he had been working since the late 1830s on the basic principles of algebra, resulting in a theory of conjugate functions, or algebraic couples, in which complex numbers are expressed as ordered pairs of real numbers.  But he hadn’t succeeded in developing a theory of triplets that could be applied to three-dimensional geometric problems.  Walking with his wife along the Royal Canal in Dublin, Hamilton realized that the theory should involve quadruplets, not triplets– at which point he stopped to carve carve the underlying equations in a nearby bridge lest he forget them.

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Written by LW

October 16, 2017 at 1:01 am

“I know numbers are beautiful. If they aren’t beautiful, nothing is”*…

 

Euler’s identity: Math geeks extol its beauty, even finding in it hints of a myste­rious connected­ness in the universe. It’s on tank tops and coffee mugs [and tattoos]. Aliens, apparently, carve it into crop circles (in 8-bit binary code). It’s appeared on The Simpsons. Twice.

What’s the deal with Euler’s identity? Basically, it’s an equation about numbers—specifically, those elusive constants π and e. Both are “transcendental” quanti­ties; in decimal form, their digits unspool into infinity. And both are ubiquitous in scientific laws. But they seem to come from different realms: π (3.14159 …) governs the perfect symmetry and closure of the circle; it’s in planetary orbits, the endless up and down of light waves. e (2.71828 …) is the foundation of exponential growth, that accelerating trajectory of escape inherent to compound interest, nuclear fission, Moore’s law. It’s used to model everything that grows…

Now, maybe you’ve never thought of math equations as “beautiful,” but look at that result: It combines the five most fundamental numbers in math—0, 1, e, i, and π—in a relation of irreducible simplicity. (Even more astonishing if you slog through the proof, which involves infinite sums, factorials, and fractions nested within fractions within fractions like matryoshka dolls.) And remember, e and π are infinitely long decimals with seemingly nothing in common; they’re the ultimate jigsaw puzzle pieces. Yet they fit together perfectly—not to a few places, or a hundred, or a million, but all the way to forever…

But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another, it lets engineers convert messy trig problems (you know, sines, secants, and so on) into more tractable algebra—like a wormhole between separate branches of math. It’s the secret sauce in Fourier transforms used to digi­tize music, and it tames all manner of wavy things in quantum mechanics, electron­ics, and signal processing; without it, computers might not exist…

More marvelous math at “The Baffling and Beautiful Wormhole Between Branches of Math.”

[TotH to @haarsager]

Paul Erdős

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As we wonder if Descartes wasn’t right when he wrote that “everything turns into mathematics,” we might spare a thought for Persian polymath Omar Khayyam; the mathematician, philosopher, astronomer, epigrammatist, and poet died on this date in 1131.  While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of the quatrains that comprise the Rubaiyat of Omar Khayyam, Omar was one of the major mathematicians and astronomers of the medieval period.  He is the author of one of the most important works on algebra written before modern times, the Treatise on Demonstration of Problems of Algebra, which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle.  His astronomical observations contributed to the reform of the Persian calendar.  And he made important contributions to mechanics, geography, mineralogy, music, climatology, and Islamic theology.

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Written by LW

December 4, 2014 at 1:01 am

Now you don’t…

Camouflage– cryptic coloration– is common in the majority of species that have lived on earth; but military camouflage is a relatively recent development.  Through the early 19th Century, almost all soldiers tended to dress in bright colors chosen precisely to make them more identifiable on the battlefield; it was during World War I that camouflage found common use.

The earliest military camouflage drew on the work of zoologist and artist Abbott Thayer, applying lessons from the animal kingdom to secreting troops and tanks.

But World War I was as importantly a naval war.  Norman Wilkinson, a marine painter [and your correspondent’s relatively distant ancestor] who was in the Royal Navy, is credited with being the first to develop camouflage for ships– “dazzle,” a kind of camouflage that is “disruptive” like zebra’s stripes. The Royal Navy allowed him to test his idea; and when the test went well, Wilkinson was told to proceed… but was given no office space.  So he went to his alma mater, the Royal Academy, and was given a classroom. Wilkinson hired Vorticist Edward Wadsworth to be a port officer in Liverpool, England and to oversee the painting of dazzle ships.  In 1918, Wilkinson came to United States to share his dazzle plans. 1,000 plans were developed through this partnership.

One of Wilkinson’s U.S. collaborators was Maurice L. Freedman, the district camoufleur for the 4th district of the U.S. Shipping Board, Emergency Fleet Corporation (a precursor to today’s Merchant Marine).  Maurice’s job was to take the plans, adjust them if necessary, then hire painters (artists, house painters) to paint the ships accordingly.

Freedman, who attended  the Rhode Island School of Design after the war, donated the plans and photos in his collection to the Fleet Library at RISD.  Now (through the end of March) those plans are on display at the library– and online.


As we dress discretely
, we might recall that it was on this date in 1258 that (a decidedly un-camouflaged) Hulagu Khan (a grandson of Genghis) and his Mongol force sacked Baghdad, and brought the Abbasid Caliphate (source of, among other marvels, algebra) to an end.

Hulagu and his Queen, Dokuz Khatun

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