Notneimanmarcus - Seriously Though. It Isn't.

In the creative mathematics, the role of proof is in no way restricted to its function of carrier of conviction. Otherwise, there would be no need for Carl Friedrich Gauss to consider eight (!) different proofs of the law of quadratic reciprocity. One metaphor of proof is a route, which might be a desert track boring and unimpressive until one finally reaches the oasis of ones destination, or a foot path in green hills, exciting and energizing, opening great vistas of unexplored lands and seductive offshoots, leading far away even after the initial destination point has been reached.

Yuri Manin, Foundations as Superstructure (Reflections of a practicing mathematician)

Mechanical Principles by Ralph Steiner (1930)

Lagrange's theorem

Theorem: The size of a subgroup of finite group is divisible by the group’s size. That is, if H is a subgroup of G, |H| is a divisor of |G|.

Proof: Let’s start by saying we have a group G and a subgroup H.

This proof will count cosets. Specifically, I’ll use left cosets, but right cosets work the same way. Also, this proof will rely on a few properties of the integers.

I’ll prove this through lemmas, which are theorems used to prove other theorems. The distinction between a lemma and a theorem is only based on how we use them, and so historical reasons might leave some theorems as “lemmas.”

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On the back roads of Glacier National Park, Montana With Andrea

Adding two identical waves, shifted by different amounts, to give a new wave. The waves interfere to either amplify each other, cancel each other out, or something in between. [more] [code]

"We humans long to be connected with our origins, so we create rituals. Science is another way to express this longing. It also connects us with our origins, and it too has its rituals and its commandments. Its only sacred truth is that there are no sacred truths. All assumptions must be critically examined. Arguments from authority are worthless. Whatever is inconsistent with the facts, no matter how fond of it we are, must be discarded or revised. Science is not perfect, it’s often misused, it’s only a tool, but it’s the best tool we have. Self-correcting, ever-changing, applicable to everything. With this tool we vanquish the impossible. With the methods of science we have begun to explore the cosmos." - Carl Sagan

This Day in Aviation History

August 22nd, 1952

First flight of the Saunders-Roe Princess flying boat.

The Saunders-Roe SR.45 Princess was a British flying boat aircraft built by Saunders-Roe, based in Cowes on the Isle of Wight. The Princess was the largest all-metal flying boat ever constructed.

The project was cancelled after having produced only three examples. By the 1950s, large, commercial flying boats were being overshadowed by land-based aircraft. Factors such as runway and airport improvements added to the viability of land-based aircraft, which did not have the weight and drag of the boat hulls on seaplanes nor the issues with seawater corrosion.

The three airframes were stored against possible purchase but when an offer was made it was found that corrosion had set in; as a result they were scrapped….

Source:

Wikipedia, Saunders-Roe Princess: http://gstv.us/1MDH8iU  

YouTube, Saunders-Roe Princess Flying Boats: http://gstv.us/1MDH9U9  

If you enjoy the “This Day in Aviation History” collection, you may enjoy some of these other collections from Gazing Skyward TV: http://gstv.us/GSTVcollections  

Photo from: http://gstv.us/2b2abBr  

#avgeek #flying #boat #SaundersRoe #Princess #British #aviation #history

Top Gear is one of the best things BBC has ever produced 

I’ve always assumed that history is fully as speculative a discipline as writing science fiction. Our narrative of history changes as we go along, and hundred years from now, the deep past—assuming that technology continues to emerge at the same rate—the deep human past that those people will be able to see will be quite unrecognizable to us.

William Gibson [x] (via edwardspoonhands)