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With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).
PDFtk (short for PDF Toolkit) is a toolkit for manipulating Portable Document Format (PDF) documents. [3] [4] It runs on Linux, Windows and macOS. [5] It comes in three versions: PDFtk Server (open-source command-line tool), PDFtk Free and PDFtk Pro (proprietary paid). [2] It is able to concatenate, shuffle, split and rotate PDF files.
If any of the above matrices, say A, is applied to a triple (a, b, c) T having the Pythagorean property a 2 + b 2 = c 2 to obtain a new triple (d, e, f) T = A(a, b, c) T, this new triple is also Pythagorean.
PDFCreator is an application for converting documents into Portable Document Format format on Microsoft Windows operating systems. It works by creating a virtual printer that prints to PDF files, and thereby allows practically any application to create PDF files by choosing to print from within the application and then printing to the PDFCreator printer.
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members.