Pythagorean ratios in arithmetic progression, part II. Four Pythagorean ratios
نویسندگان
چکیده
منابع مشابه
Pythagorean Triples
Let n be a number. We say that n is square if and only if: (Def. 3) There exists m such that n = m2. Let us note that every number which is square is also natural. Let n be a natural number. Note that n2 is square. Let us observe that there exists a natural number which is even and square. Let us observe that there exists a natural number which is odd and square. Let us mention that there exist...
متن کاملPythagorean Triples
The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...
متن کاملPythagorean Descent
where B(v, w) = 12(Q(v + w) − Q(v) − Q(w)) is the bilinear form associated to Q. The transformation sw is linear, fixes the plane w⊥ = {v : v ⊥ w}, and acts by negation on the line through w. These properties characterize sw. We will use reflections associated to the four vectors e1 = (1, 0, 0), e2 = (0, 1, 0), e3 = (0, 0, 1), and e1 + e2 + e3 = (1, 1, 1). The vectors e1, e2, and e3 form an ort...
متن کاملPythagorean powers of hypercubes
For n ∈ N consider the n-dimensional hypercube as equal to the vector space F2 , where F2 is the field of size two. Endow F2 with the Hamming metric, i.e., with the metric induced by the `1 norm when one identifies F2 with {0, 1} ⊆ R. Denote by `2 (F2 ) the n-fold Pythagorean product of F2 , i.e., the space of all x = (x1, . . . , xn) ∈ ∏n j=1 F n 2 , equipped with the metric ∀x, y ∈ n ∏ j=1 F2...
متن کاملPrime Pythagorean triangles
A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequence. We exhibit a chain of seven prime Pythagorean triangles and we include a brief discussion of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1994
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500030536