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The Egyptian Berlin Papyrus, dating back to the Middle Kingdom (2050 BC to 1650 BC), contains the solution to a two-term quadratic equation. [21] Babylonian mathematicians from circa 400 BC and Chinese mathematicians from circa 200 BC used geometric methods of dissection to solve quadratic equations with positive roots.
The universal halting problem, also known (in recursion theory) as totality, is the problem of determining whether a given computer program will halt for every input (the name totality comes from the equivalent question of whether the computed function is total). This problem is not only undecidable, as the halting problem is, but highly ...
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
TRIZ flowchart Contradictions matrix 40 principles of TRIZ. One tool which evolved as an extension of TRIZ was a contradiction matrix. [14] The ideal final result (IFR) is the ultimate solution of a problem when the desired result is achieved by itself.
These studies were conducted largely based on individual problem solving of well-defined problems. Sweller (1988) proposed cognitive load theory to explain how novices react to problem solving during the early stages of learning. [41] Sweller, et al. suggests a worked example early, and then a gradual introduction of problems to be solved.
Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle in a weighted graph with the minimal weight of the weightiest edge. A real-world example is avoiding narrow streets with big buses. [15] The problem is of considerable practical importance, apart from evident transportation and logistics areas.
If an equation can be put into the form f(x) = x, and a solution x is an attractive fixed point of the function f, then one may begin with a point x 1 in the basin of attraction of x, and let x n+1 = f(x n) for n ≥ 1, and the sequence {x n} n ≥ 1 will converge to the solution x.
The scientific method embodies the position that reason alone cannot solve a particular scientific problem; it unequivocally refutes claims that revelation, political or religious dogma, appeals to tradition, commonly held beliefs, common sense, or currently held theories pose the only possible means of demonstrating truth.