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In mathematics, a tree of primitive Pythagorean triples is a data tree in which each node branches to three subsequent nodes with the infinite set of all nodes giving all (and only) primitive Pythagorean triples without duplication.
Generating all primitive Pythagorean triples using half-angle tangents. A primitive Pythagorean triple can be reconstructed from a half-angle tangent. Choose r, a positive rational number in (0, 1), to be tan A/2 for the interior angle A that is opposite the side of length a.
The basic anatomy of a millstone. This is a runner stone; a bedstone would not have the "Spanish Cross" into which the supporting millrind fits. Millstones or mill stones are stones used in gristmills, used for triturating, crushing or, more specifically, grinding wheat or other grains. They are sometimes referred to as grindstones or grinding ...
Numeral systems. Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.
Diphasiastrum digitatum is known as groundcedar, running cedar or crowsfoot, along with other members of its genus, but the common name fan clubmoss can be used to refer to it specifically. It is the most common species of Diphasiastrum in North America. It is a type of plant known as a clubmoss, which is within one of the three main divisions ...
Primitive translation vectors for this simple hexagonal Bravais lattice vectors are a 1 = 3 2 a x ^ + 1 2 a y ^ , a 2 = − 3 2 a x ^ + 1 2 a y ^ , a 3 = c z ^ . {\displaystyle {\begin{aligned}a_{1}&={\frac {\sqrt {3}}{2}}a{\hat {x}}+{\frac {1}{2}}a{\hat {y}},\\[8pt]a_{2}&=-{\frac {\sqrt {3}}{2}}a{\hat {x}}+{\frac {1}{2}}a{\hat {y}},\\[8pt]a_{3 ...