![]() In geometry, a polyhedron (plural polyhedra or polyhedrons) is solid with flat polygonal faces, straight edges, and sharp corners or vertices. In December 2014, PSY’s music video “Gangnam Style” had exceeded the 32-bit integer limit for YouTube view count, necessitating YouTube to upgrade the counter to a 64-bit integer. It is, therefore, the maximum value for variables declared as integers (e.g., as int) in many programming languages, and the maximum possible score, money, etc. Photograph: Science and Society Picture Library The most prolific mathematician of all time, publishing close to 900 books. The number 2,147,483,647 (or hexadecimal 7FFF,FFFF16) is the maximum positive value for a 32-bit signed binary integer in computing. It remained the largest known prime until 1867. That is, it is a prime number of the form Mn = 2 n − 1 for some integer n.īy 1772, Euler had proved that 2³¹ − 1 = 2,147,483,647 is a Mersenne prime. In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ![]() In the third representation of bridges in the graphical form, it is visible that there are no such nodes. ![]() The only nodes that can have an odd number of links attached to them are the nodes where the walk starts and ends (if they are distinct). That’s because whenever you enter the node by one link, you need to leave it by another, so the node needs two links if you visit it once, four if you visit it twice, and so on. “Approximately one-third of the entire corpus of research on mathematics and mathematical physics and engineering mechanics published in the last three-quarters of the eighteenth century is by him.” - Clifford TruesdellĮuler observation: If a path through this network is going to cross every link exactly once, then each node within the path must have an even number of links attached to it. His efforts to standardize these and other symbols (including π and the trigonometric functions) helped to internationalize mathematics and to encourage collaboration on problems. Much of the notation used by mathematicians today - including e, i, f( x), ∑, and the use of a, b and c as constants and x, y and z as unknowns - was either created, popularized or standardized by Euler. ![]() He authored over 800 papers, his collected works fill 92 volumes, more than anyone else in the field and that too after going blind. “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.” - Leonhard EulerĮuler was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who made important and influential discoveries in many branches of mathematics.īut what makes him great in the first place? ![]()
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