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Thus one can view (4) as a “master equation” for spherical trigonometry: in principle, it can be used to derive all the other laws of this subject. Remark 1 The law (4) has an evident symmetry , which corresponds to the operation of replacing a spherical triangle with its dual ...
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers: ...
diamond is the hardest known mineral. it is a high-symmetry allotrope of carbon (c). it has a mohs “scratch” hardness of 10, which makes it the hardest mineral. mohs hardness is a rough measure of the resistance of a smooth surface to scratching or abrasion, expressed in terms of ...
cloud once more. There was but one explanation. It was Mallory and his companion moving, as I could see even at that great distance, with considerable alacrity … The place on the ridge referred to is the prominent rock-step at a very short distance from the base of the final pyramid...
Re: what is going on! =( « Reply #5 on: January 27, 2012, 08:51:24 AM » Where did you get the equation r=(cube root of the atomic number) x (1.2x10^-15 m)? This completely ignores the contribution of neutrons. It should be the atomic mass number, the number of proton...
While they are non-commutative, they do keep many other properties of the complex numbers: Being non-commutative, the quaternions do not form a field. However, they are still a skew field (or division ring): multiplication is associative, and every non-zero quaternion has a unique ...
The last two elements of both sequences are new; the computation was the hardest and required a non-trivial amount of computer assistance. We also establish the asymptotic lower bounds and . In contrast, the best known upper bound to these quantities is , obtained by the sister project to ...
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing Books Applets Mastodon+ Subscribe to feed Books In these pages are the latest information (including sample chapters and errata) for all th...
On the other hand, it can be worth researchingwhya problem or mathematician is famous, orhowan institution or department earnt its prestige; such specific information can help you decide whether this problem, mathematician, or department would be of interest to you. See also “Which universities...