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Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well.
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
Pages in category "Unsolved problems in geometry" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. A.
The question of minimizing the number of crossings in drawings of complete bipartite graphs is known as Turán's brick factory problem, and for , the minimum number of crossings is one. K 3 , 3 {\displaystyle K_{3,3}} is a graph with six vertices and nine edges, often referred to as the utility graph in reference to the problem. [ 1 ]
This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8] The general trisection problem is also easily solved when a straightedge with two marks on it is allowed (a neusis construction).
Graham's number, one of the largest numbers ever used in serious mathematical proof, is an upper bound for a problem related to Ramsey theory. Another large example is the Boolean Pythagorean triples problem. [3] Theorems in Ramsey theory are generally one of the following two types.
In finite geometry, PG(3, 2) is the smallest three-dimensional projective space. It can be thought of as an extension of the Fano plane. It has 15 points, 35 lines, and 15 planes. [1] It also has the following properties: [2] Each point is contained in 7 lines and 7 planes. Each line is contained in 3 planes and contains 3 points.
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