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Volume 108

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Volume 108 - July 2024

Notes

108.05 Ramanujan’s proof of Bertrand’s postulate

108.24 Covering a triangular number with heptagonal numbers

108.25 A pair of interesting inequalities for ex

108.06 Simple bounds on a sum pertinent to primes

108.07 De Moivre’s theorem via difference equations

108.26 PWW: A property of triangular numbers

108.08 Cone and Integral

108.27 More on the Euler limit for e

108.09 A visual proof that be < eb when b > e

108.28 π is a mean of 2 and 4

108.10 Proof without words: ${\rm{tan }}{\pi\over {{\rm{12}}}}{\rm{=2 - }}\sqrt 3 {\rm{, tan }}{{{\rm{5}}\pi } \over {{\rm{12}}}}{\rm{=2 + }}\sqrt {\rm{3}} $

108.29 A geometric mean–arithmetic mean ratio limit

108.30 Nearly isosceles right-angled triangles and square triangular numbers

108.11 Euler’s limit—revisited

108.12 Proof without words: a lower bound for n!

108.31 Generalised Thales intercept theorem

108.13 Indeterminate exponentials without tears

108.32 Point masses and polygons

108.33 Some inequalities for a triangle

108.14 A triangle number identity

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Volume 108 - July 2024

Notes