Posts Tagged ‘Omar Khayyam’
“In Japanese and Italian, the response to [‘How are you?’] is ‘I’m fine, and you?’ In German it’s answered with a sigh and a slight pause, followed by ‘Not so good’.”*…
If you own a smartphone and are trying to learn a language, you probably have Duolingo. At this very moment the app—which tries to turn language learning into a rewarding game—may be not-so-subtly suggesting that you are overdue for some Spanish vocabulary practice.
How many other people are learning Spanish, and where do they live?Duolingo recently answered such questions by running the numbers on their 120 million users, spanning every country on the planet. The company identified the most popular language for each country, among the 19 it offers…
More at “The languages the world is trying to learn, according to Duolingo.” [Note the absence of Mandarin, Japanese, Arabic and other Asian and Middle Eastern languages– surely a reflection, at least in large part, of the offers available on Duolingo, which teaches in more languages than it teaches…]
* David Sedaris, Let’s Explore Diabetes with Owls
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As we prepare to conjugate, we might send elegantly phrased and eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. 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 treatises 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.
“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]
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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.
Now let us praise famous men (and women)…
From Aitken’s to Zipf’s— some of them coined by their namesake (e.g., Parkinson’s); others, based on their work or publications (a la Moore’s): consider the rules, adages, observations, and predictions that make up The List of Eponymous Laws.
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As we take the oath, we might spare a thought for Persian polymath Omar Khayyam; the philosopher, mathematician, 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 treatises 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.
Everything goes better with sharks…
Sharks!
Given the successes of “Shark Week” and Sharknado, it’s a sure bet that Hollywood will move to remake the classics to feature those creepily-cartilaginous predators. See what to expect at Sharks Make Movies Better.
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As we decide that it isn’t yet, perhaps, safe to go back into the water, we might might send carefully-calculated birthday greetings to Giovanni Girolamo Saccheri; he was born on this date in 1667. A Jesuit priest and Scholastic philosopher, Saccheri is probably best remembered for his attempt to disprove the fifth postulate of Euclid (“through any point not on a given line, one and only one line can be drawn that is parallel to the given line”). In fact, Saccheri’s thinking closely mirrored that of Omar Khayyám’s 11th Century Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb ‘Uglîdis)– though it’s not clear that Saccheri knew the earlier work.
In any case, Saccheri’s Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw, 1733) helped lay the foundation for what we now call Non-Euclidean Geometry.
The Widening Gyre…
click here, and again, for larger version at source
TURNING and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.Surely some revelation is at hand;
Surely the Second Coming is at hand.
The Second Coming! Hardly are those words out
When a vast image out of Spiritus Mundi
Troubles my sight: somewhere in sands of the desert
A shape with lion body and the head of a man,
A gaze blank and pitiless as the sun,
Is moving its slow thighs, while all about it
Reel shadows of the indignant desert birds.
The darkness drops again; but now I know
That twenty centuries of stony sleep
Were vexed to nightmare by a rocking cradle,
And what rough beast, its hour come round at last,
Slouches towards Bethlehem to be born?– “The Second Coming,” W.B. Yeats
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As we remark that the spiral will continue we know not where, we might send eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. 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 treatises 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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