*This capsule discusses a way to show each non-zero element of certain rings have a multiplicative inverse. The approach is to set up a system of linear equations and the solution is the...*

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Displaying 31 - 40 of 1212

*In how many ways can a pet photographer pose \(C\) cats, \(D\) dogs, and \(E\) emus? The problem, often called Smirnov`s problem, has several practical applications and has been solved...*

*A visualization of the triple angle formulas for sines and cosines is presented.*

*The limit of the geometric mean of the first \(n\) integers raised to the real positive power \(s\), divided by their arithmetic mean is shown to be \((s+1)/e^s\). An elementary derivation of...*

*The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...*

*The author gives a visual proof of the Pythagorean Theorem.*

*The author presents a geometric interpretation of Leibniz's rule for differentiating under the integral sign, and gives an informal visual derivation of the rule. *

*Using basic linear algebra, the authors obtain a complete, easy to compute, winning strategy for the \(4 \times 4\) mini `Lights Out` game.*

*The theorem, “An infinite group is cyclic when each of its nonidentity subgroups have finite index,” is proved and discussed, and a test to show groups are not cyclic is ...*

*The author gives a proof of the title as an application of Lagrange`s Theorem, allowing the theorem to be presented in the first semester of an undergraduate abstract algebra course.*