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by Jeff Johnson The universe can be a very strange place. While groundbreaking ideas such as quantum theory, relativity and even the Earth going around the Sun might be commonly accepted now, science still continues to show that the universe contains things you might find it difficult to believe, and even more difficult to get your head around. Theoretically, the lowest temperature that can be achieved is absolute zero, exactly −273.15°C, where the motion of all particles stops completely. However, you can never actually cool something to this temperature because, in quantum mechanics, every particle has a minimum energy, called “zero-point energy,” which you cannot get below. Remarkably, this minimum energy doesn’t just apply to particles, but to any vacuum, whose energy is called “vacuum energy.”
10 Strange Things About The Universe - Top 10 Lists | Listverse
There’s a powerful integration trick that I don’t believe is too widely known. Some calculus books mention it in a footnote, but few emphasize it. This is unfortunate since this trick applies to more problems than many of the more ad hoc techniques that are commonly taught. Karl Weierstrass (1815-1897) came up with the idea of using t = tan( x /2) to convert trig functions of x to rational functions of t . If t = tan( x /2), then
Sledgehammer technique for trig integrals — The Endeavour
