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Robbins Pentagon
In geometry, a Robbins pentagon is a cyclic pentagon whose side lengths and area are all rational numbers. History Robbins pentagons were named by after David P. Robbins, who had previously given a formula for the area of a cyclic pentagon as a function of its edge lengths. Buchholz and MacDougall chose this name by analogy with the naming of Heron triangles after Hero of Alexandria, the discoverer of Heron's formula for the area of a triangle as a function of its edge lengths. Area and perimeter Every Robbins pentagon may be scaled so that its sides and area are integers. More strongly, Buchholz and MacDougall showed that if the side lengths are all integers and the area is rational, then the area is necessarily also an integer, and the perimeter A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robbins Pentagon1
Robbins may refer to: People * Robbins (name), a surname Fictional characters * Al Robbins, medical doctor in ''CSI: Crime Scene Investigation'' * Arizona Robbins, surgeon in ''Grey's Anatomy'' * Ashley Mizuki Robbins, protagonist in the video games '' Another Code: Two Memories'' and '' Another Code: R – A Journey into Lost Memories'' * Jack Robbins, character on ''EastEnders'' television series * Lily Robbins, character in ''The Lily Series'' * Parker Robbins, comic book character Places Antarctica * Robbins Hill, a hill at the terminus of Blue Glacier Australia * Robbins Passage and Boullanger Bay Important Bird Area, Tasmania USA * Robbins, California, town in Sutter County * Robbins, Illinois, village in Cook County * Robbins, Michigan, an unincorporated community * Robbins, Missouri, an unincorporated community * Robbins, North Carolina, city in Moore County * Robbins, Tennessee, unincorporated community in Scott County *Robbins, Virginia, ghost town Other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perimeter
A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter. Formulas The perimeter is the distance around a shape. Perimeters for more general shapes can be calculated, as any path, with \int_0^L \mathrms, where L is the length of the path and ds is an infinitesimal line element. Both of these must be replaced by algebraic forms in order to be practically calculated. If the perimeter is given as a closed piecewise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Problems Of Plane Geometry
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the impleme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief is Vadim Ponomarenko (San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have been editor-in-chief: See also *''Mathematics Magazine'' *''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete And Computational Geometry
'' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational geometry. Abstracting and indexing The journal is indexed in: * ''Mathematical Reviews'' * ''Zentralblatt MATH'' * ''Science Citation Index'' * ''Current Contents'' Notable articles Two articles published in ''Discrete & Computational Geometry'', one by Gil Kalai in 1992 with a proof of a subexponential upper bound on the diameter of a polytope and another by Samuel Ferguson in 2006 on the Kepler conjecture on optimal three-dimensional sphere packing, earned their authors the Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Number Theory
The ''Journal of Number Theory'' (''JNT'') is a monthly peer-reviewed scientific journal covering all aspects of number theory. The journal was established in 1969 by R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus (Ohio State University). It is currently published monthly by Elsevier and the editor-in-chief is Dorian Goldfeld (Columbia University). According to the ''Journal Citation Reports'', the journal has a 2022 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 0.7. David Goss prize The David Goss Prize in Number theory, founded by the Journal of Number Theory, is awarded every two years, to mathematicians under the age of 35 for outstanding contributions to number theory. The prize is dedicated to the memory of David Goss who was the fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heronian Triangle
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths , , and and area are all positive integers. 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 and area . Heron's formula implies that the Heronian triangles are exactly the positive integer solutions of the Diophantine equation :16\,A^2=(a+b+c)(a+b-c)(b+c-a)(c+a-b); that is, the side lengths and area of any Heronian triangle satisfy the equation, and any positive integer solution of the equation describes a Heronian triangle. If the three side lengths are setwise coprime (meaning that the greatest common divisor of all three sides is 1), the Heronian triangle is called ''primitive''. Triangles whose side lengths and areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called ''Heronian triangles'' or ''rational triangles''; in this art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not.. For example, −4, 0, and 82 are even numbers, while −3, 5, 23, and 69 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with decimals or fractions like 1/2 or 4.6978. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heron's Formula
In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, s = \tfrac12(a + b + c), the area is A = \sqrt. It is named after first-century engineer Heron of Alexandria (or Hero) who proved it in his work ''Metrica'', though it was probably known centuries earlier. Example Let be the triangle with sides , , and . This triangle's semiperimeter is s = \tfrac12(a+b+c)= \tfrac12(4+13+15) = 16 therefore , , , and the area is \begin A &= \\ mu&= \\ mu&= 24. \end In this example, the triangle's side lengths and area are integers, making it a Heronian triangle. However, Heron's formula works equally well when the side lengths are real numbers. As long as they obey the strict triangle inequality, they define a triangle in the Euclidean plane whose area is a positive real number. Alternate expressions Heron's formula can also be written in terms of just ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robbins Pentagon2
Robbins may refer to: People * Robbins (name), a surname Fictional characters * Al Robbins, medical doctor in ''CSI: Crime Scene Investigation'' * Arizona Robbins, surgeon in ''Grey's Anatomy'' * Ashley Mizuki Robbins, protagonist in the video games '' Another Code: Two Memories'' and '' Another Code: R – A Journey into Lost Memories'' * Jack Robbins, character on ''EastEnders'' television series * Lily Robbins, character in ''The Lily Series'' * Parker Robbins, comic book character Places Antarctica * Robbins Hill, a hill at the terminus of Blue Glacier Australia * Robbins Passage and Boullanger Bay Important Bird Area, Tasmania USA * Robbins, California, town in Sutter County * Robbins, Illinois, village in Cook County * Robbins, Michigan, an unincorporated community * Robbins, Missouri, an unincorporated community * Robbins, North Carolina, city in Moore County * Robbins, Tennessee, unincorporated community in Scott County *Robbins, Virginia, ghost town Other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hero Of Alexandria
Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity and a representative of the Hellenistic scientific tradition. Hero published a well-recognized description of a steam-powered device called an '' aeolipile'', also known as "Hero's engine". Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land. In his work ''Mechanics'', he described pantographs. Some of his ideas were derived from the works of Ctesibius. In mathematics, he wrote a commentary on Euclid's ''Elements'' and a work on applied geometry known as the ''Metrica''. He is mostly remembered for Heron's formula; a way to calculate the area of a triangle using only the lengths of its sides. Much of Hero's original writings and designs have been lost, bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heron Triangle
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths , , and and area are all positive integers. 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 and area . Heron's formula implies that the Heronian triangles are exactly the positive integer solutions of the Diophantine equation :16\,A^2=(a+b+c)(a+b-c)(b+c-a)(c+a-b); that is, the side lengths and area of any Heronian triangle satisfy the equation, and any positive integer solution of the equation describes a Heronian triangle. If the three side lengths are setwise coprime (meaning that the greatest common divisor of all three sides is 1), the Heronian triangle is called ''primitive''. Triangles whose side lengths and areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called ''Heronian triangles'' or ''rational triangles''; in this arti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
