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In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [1] [2] Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides 13, 14, 15 and area 84.
A least common multiple of a and b is a common multiple that is minimal, in the sense that for any other common multiple n of a and b, m divides n. In general, two elements in a commutative ring can have no least common multiple or more than one. However, any two least common multiples of the same pair of elements are associates. [10]
A plot of triples generated by Euclid's formula maps out part of the z 2 = x 2 + y 2 cone. A constant m or n traces out part of a parabola on the cone. Euclid's formula [3] is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers
Lowest common factor may refer to the following mathematical terms: Greatest common divisor, also known as the greatest common factor; Least common multiple;
The ratio p/q takes its greatest value, 12/5=2.4, in Row 1 of the table, and is therefore always less than +, a condition which guarantees that p 2 − q 2 is the long leg and 2pq is the short leg of the triangle and which, in modern terms, implies that the angle opposite the leg of length p 2 − q 2 is less than 45°. The ratio is least in ...
A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).
An automedian triangle is one whose medians are in the same proportions (in the opposite order) as the sides. If x, y, and z are the three sides of a right triangle, sorted in increasing order by size, and if 2x < z, then z, x + y, and y − x are the three sides of an automedian triangle. For instance, the right triangle with side lengths 5 ...
In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...