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Posts Tagged ‘topology

“In a flat country a hillock thinks itself a mountain”*…

In 2003, the Annals of Improbable Research released the results of a study that was not so much groundbreaking as it was ground-battering: Kansas, the tongue-in-cheek analysis found, was flatter than a pancake. The researchers Mark Fonstad, William Pugatch, and Brandon Vogt used polynomial equations to calculate the flatness of the famously flat state, and discovered that—as compared to the topography of an IHOP pancake—it was indeed flatter than a flapjack.

Their finding was not incorrect. Parts of Kansas are, in fact, flatter than a pancake! But the study’s focus on Kanas, it turns out, was also misleading. Because there are states—six of them, to be specific—that are even flatter than Kansas. The states flatter than a pancake, you could say, could be served in a short stack.

This latest flatness finding comes courtesy of geographers at the University of Kansas, who just published a paper, “The Flatness of U.S. States,” inGeographical Review, a peer-reviewed journal published by the American Geographical Society…

The top 10 flattest states, per their results? [Results charted on the map above differ as they reflect a slightly different analysis; c.f., the link below.]

Florida

Illinois

North Dakota

Louisiana

Minnesota

Delaware

Kansas

Texas

Nevada

Indiana

Get level at “Science: Several U.S. States, Led by Florida, Are Flatter Than a Pancake.”

* Turkish proverb

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As we reach for the maple syrup, we might send lofty birthday greetings to Albert William Stevens; he was born on this date in 1886.  An career officer in the U.S. Army Air Corps. Stevens was a pioneering balloonist and aerial photographer who took the first photograph clearly showing the Earth’s curvature (1930) and the first photographs of the Moon’s shadow on the Earth during a solar eclipse (1932).  In 1935 Stevens and a colleague made a record balloon ascent near Rapid City, South Dakota.  20,000 watched– and millions listened to a live NBC broadcast– as their sealed gondola, Explorer II, climbed to 72,395 feet, nearly 14 miles, a record that stood until 1956.

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Written by LW

March 13, 2014 at 1:01 am

“The future ain’t what it used to be….”*

Just over a hundred years ago, in 1910, the Cedar Rapids Evening Gazette in Iowa published a list of advances and innovations that they believed would appear during the century, a fascinating list of things scientific/technical and social/political:

  • Cure for cancer.
  • Discovery south pole.
  • Prevent or cure insanity.
  • Influence sex by parental treatment.
  • Create living organisms by artificial means.
  • Phonograph records substitute for letter.
  • Rationing clothing reform, health, comfort, durability only considerations
  • Settle question of communication with Mars. Wonderful astronomical discoveries.
  • Power of mind over matter a practical science devoid of superstitious elements.
  • United States constitution rewritten, providing improved means for conservation of original democratic principles.
  • Marvelous progress in transportation, largely aerial; airships and dirigible balloons crossing oceans and continents in remarkable time. Racing planes make five miles per minute. Inland waterways carry slow freight by improved methods. Monorail supplants two tracks. Electricity replaces steam. Convenient, economical city traffic system broadens city areas, opening suburban lands to householders. Pneumatic tubes for mails and express. Horses curiosities. Automobiles relegated to short distance burden bearing. Ocean steamers for freight, improvement toward speed rather than size.
  • Produce rainfall at will.
  • Temper gold and copper.
  • Roads of nation paved.
  • Conservation of sun’s heat and power.
  • Cure for and elimination of tuberculosis.
  • Development psychic research with fraud eliminated.
  • Movements for universal language, universal religion, universal money.
  • Non-existence of blindness by eliminating causes except accidents.
  • Construction largely of concrete and metal or newly discovered materials.
  • Electricity will move world’s wheels. Later radio-activity may substitute.
  • Terrors of war so multiplied by death dealing inventions, chances of war minimized.
  • Utilization of all energy, reducing consumption of wood and coal. Many fuel substitutes.
  • Population of United States based on present ratio of increased, 1,317,547,000 at opening of twenty-first century.
  • Rational diet with greatly reduced consumption of matter with increased nourishment from proper mastication and choices of foods.
  • Machinery largely substituting manual energy, will promote pursuit of finer arts and sciences; give ample opportunity for relaxation and amusement; emancipate wage slaves. Three-hour work day predicted.
  • Sea water for irrigation.
  • Photographs in natural colors.
  • Women’s political equality.
  • Government control of corporations.
  • Animated pictures in natural colors, transmitted by wireless.
  • Substitution of heavier metals with aluminum, etc.
  • Natural colors reproduced in newspaper pictures.
  • Reduction of elimination all forms of gambling, including stocks.
  • General acceptance of public ownership or control of public utilities.
  • Government operation banking system, elimination of private banks. Postal savings banks.
  • Moral, intellectual and economical awakening in dark sections of Africa, China a world power.
  • Beautiful and healthful cities, offering with homes and work places all forms of free amusement, culture and recreation.
  • Greater premium on brains with corresponding decreased in respect for position not gained by individual achievement.
  • Revision judicial system, deciding causes on improved scientific plan, insuring equal justice. Pathological and psychological treatment for criminals. Crime reduced.
  • Due to universal education, with special reference to hygiene, doctors and drugs be largely eliminated; average age to be near 60 years; men taller, stronger, higher intelligence and morals.

Some of their predictions were spot on (“Natural colors reproduced in newspaper pictures”); some, sadly as yet unrealized (“Cure for cancer”); and some, ironically backwards (“Government control of corporations”). But overall, it’s consoling to be reminded that things that seem wild, even radical at one moment in time– in this case, things like women’s rights and child labor laws– can, with the passage of time, become so obvious as to become human rights that we take for granted.

[TotH to Paleofuture, from whence the illustration above; via the always-excellent Next Draft]

* Yogi Berra

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As we live in the past, we might send twisted birthday greetings to August Ferdinand Möbius; he was born on this date in 1790.  A mathematician and theoretical astronomer, Möbius was so important to the fields of analytic geometry, topology, and number theory that several mathematical concepts are named after him, including the Möbius configuration, the Möbius transformations, the Möbius transform, the Möbius function μ(n), and the Möbius inversion formula

But he is best remembered, of course, as the creator of the Möbius Strip— a two-dimensional surface with only one side…. more specifically: a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space… It can be constructed in three dimensions: Take a rectangular strip of paper and join the two ends of the strip together so that it has a 180 degree twist. It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other side of the surface from A.

 source

 

Written by LW

November 17, 2013 at 1:01 am

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