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searching for Pythagorean Triangles 20 found (30 total)

Sum of squares (702 words) [view diff] case mismatch in snippet view article find links to article

sums of two squares states which primes are Pythagorean primes. Pythagorean triangles with integer altitude from the hypotenuse have the sum of squares

65 (number) (852 words) [view diff] case mismatch in snippet view article

33 + 42 + 51. 65 is the length of the hypotenuse of 4 different Pythagorean triangles, the lowest number to have more than 2: 652 = 162 + 632 = 332 +

Nonhypotenuse number (447 words) [view diff] exact match in snippet view article find links to article

Beiler, Albert H. (1968), "Albert Beiler, Consecutive Hypotenuses of Pythagorean Triangles", Mathematics of Computation, 22 (103): 690–692, doi:10.2307/2004563

85 (number) (883 words) [view diff] case mismatch in snippet view article

ways, 85 = 92 + 22 = 72 + 62. the length of the hypotenuse of four Pythagorean triangles. a Smith number in decimal. Messier object M85 is a magnitude 10

Fermat's right triangle theorem (2,278 words) [view diff] case mismatch in snippet view article find links to article

were themselves square. By rearranging the equations for the two Pythagorean triangles above, and then multiplying them together, one obtains the single

Proof by infinite descent (2,224 words) [view diff] case mismatch in snippet view article find links to article

than 1) Pythagorean triangle with the same property. Primitive Pythagorean triangles' sides can be written as x = 2 a b , {\displaystyle x=2ab,} y =

Al-Firdaws Madrasa (1,492 words) [view diff] case mismatch in snippet view article find links to article

3-4-5 ratio in which a rectangular area was made by combining two pythagorean triangles. The heights of the building's columns shared the same measurement

Noether Lecture (295 words) [view diff] exact match in snippet view article find links to article

Survey of Coding Theory 1981 Olga Taussky-Todd The Many Aspects of Pythagorean Triangles 1982 Julia Robinson Functional Equations in Arithmetic 1983 Cathleen

60 (number) (1,512 words) [view diff] case mismatch in snippet view article

"Sequence A063011 (Ordered products of the sides of primitive Pythagorean triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation

Sierpiński triangle (2,673 words) [view diff] case mismatch in snippet view article find links to article

cut-the-knot Real-time GPU generated Sierpinski Triangle in 3D Pythagorean triangles, Waclaw Sierpinski, Courier Corporation, 2003 A067771 Number

Group of rational points on the unit circle (1,226 words) [view diff] exact match in snippet view article find links to article

Vol. 69, No. 3 (June, 1996), pp. 163–171 The Group of Primitive Pythagorean Triangles[2], Ernest J. Eckert, Mathematics Magazine Vol 57 No. 1 (January

Automedian triangle (1,664 words) [view diff] case mismatch in snippet view article find links to article

triangle. Consequently, using Euler's formula that generates primitive Pythagorean triangles it is possible to generate primitive integer automedian triangles

List of works designed with the golden ratio (4,398 words) [view diff] case mismatch in snippet view article find links to article

considered that setting out also involved the use of equilateral or Pythagorean triangles, pentagons, and octagons. Two authors believe the Golden Section

700 (number) (3,993 words) [view diff] case mismatch in snippet view article

J. A. (ed.). "Sequence A024364 (Ordered perimeters of primitive Pythagorean triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation

Lambek–Moser theorem (2,425 words) [view diff] case mismatch in snippet view article find links to article

JSTOR 40148160, MR 1189138 Wild, Roy E. (1955), "On the number of primitive Pythagorean triangles with area less than n", Pacific Journal of Mathematics, 5: 85–91

1000 (number) (25,218 words) [view diff] case mismatch in snippet view article

Germain prime, super-prime 1500 = hypotenuse in three different Pythagorean triangles 1501 = centered pentagonal number 1502 = number of pairs of consecutive

Fibonacci sequence (12,887 words) [view diff] case mismatch in snippet view article find links to article

(F_{n}F_{n+3})^{2}+(2F_{n+1}F_{n+2})^{2}={F_{2n+3}}^{2}.} The sequence of Pythagorean triangles obtained from this formula has sides of lengths (3,4,5), (5,12,13)

Hallstatt culture (8,521 words) [view diff] case mismatch in snippet view article find links to article

in Denmark (0.7855 m), dating from the Bronze Age (c. 1350 BC). Pythagorean triangles were likely used in building construction to create right angles

Formulas for generating Pythagorean triples (4,743 words) [view diff] case mismatch in snippet view article find links to article

Price, H. Lee (2005). "Heron's formula, Descartes circles, and Pythagorean triangles". arXiv:math/0701624v1. Price, H. Lee (2008). "The Pythagorean Tree:

Heronian triangle (5,843 words) [view diff] case mismatch in snippet view article find links to article

There are Heronian triangles that cannot be obtained by joining Pythagorean triangles. For example, the Heronian triangle of side lengths 5 , 29 , 30