*A short proof of the well-known fact that the unit interval \([0,1]\) is uncountable is presented by means of a simple infinite game. The author also used this game to show that a (non-empty)...*

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Displaying 1011 - 1020 of 1212

*Various examples of convergent Newton sequences which do not converge to a zero of the underlying function are given.*

*The author discusses an intuitive direct proof of the fact that functions with zero derivative must be constant, which turns into a rigorous proof by simply invoking the completeness of the...*

*Infinite series representing several functions, and several series representing \(\pi\) are derived using tabular integration by parts.*

*Three lemmas of interest in themselves from which Euler's Triangle Inequality follows are proved wordlessly.*

*A triangle labeled two different ways verifies the double angle formula for sines.*

*The authors discuss ways to induce students to recognize the use of symmetry to evaluate challenging integrals, and to prevent student sidesteps. *

*The author gives a synthetic geometric proof answering the question in the title of the paper.*

*The author uses the golden matrix ring \(Z(A)\) generated by \(A= \left[ \begin{array}{cccc} 0 & 1 \\ 1 & 1 \end{array} \right] \) to prove certain identities involving Fibonacci...*