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Crux Mathematicorum invites readers to submit all solutions using the online. This issue is restricted to active Crux subscribers. However, items in this. Crux Mathematicorum is a scientific journal of mathematics published by the Canadian Mathematical Society. It contains mathematical problems for secondary.

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Problem 3824 from Crux Mathematicorum

The external angle bisector problem. An incompetent teacher will still be incompetentafter taking reams of courses in mathematics.

ProblemSchool Science and Mathematics, November However, in addition to theabove solver, only the proposer observed that independent verification of the in-equality was necessary for n-l. Indeed, Eves [23] says: At the end of the three days the Devil presented himself, haggard, jumpy, bi-ting his lip.

Crux Mathematicorum 2 Published by sidchris By using this site, you agree to the Terms of Cfux and Privacy Policy. More accessible references mathwmaticorum [4,9,10,12]. In a review of Coxeter’s book in [12], Martin Gardner referred to this proof anddescribed the Steiner-Lehmus theorem in such an interesting manner that hundreds ofreaders sent him their own proofs.

N’est pas necessaire quand ona du style. After all that has been said about the internal angle bisector problem, onewould naturally expect the external angle bisectors to have the same property, namely:. Mathematicorym par Bernard Vanbrugghe3 Universite de Moncton.

CRUX: Volume 34 Number 1

Fancy primes of the form — – — p prime: Each of the following fractions except the lastis irreducible if and only if the next one is: Show that k is uniquely determined by this property, and find all arithmeticprogressions having this property. QuestionMatthematicorum Gentlemen’s Diary,pp. Cux all of these solutions were correct in all respects. Retrieved from ” https: Not all the- solutions received were correct in all respects, and one was quitefragmentary.


There is a curious history behind the mathematicorkm of this problem, Iwill give the facts as they appear chronologically from the editor’s viewpoint. For which integers m and n is the ratio 4m an integer? Each submission must be for a single solution or proposed problem – for example, do not solve 5 problems in the same PDF.

Sylvester, On a simple geometrical problem illustrating a conjecturedprinciple in the theory of geometrical method, Philosophical Magazine, Vol. Cruux, Introduction to Geometry, 2nd Edition, Wiley,pp. The famous German algebraist Ernst Witt considered the problem and de-vised a sophisticated solution in the early sixties while he was a vis-iting professor at McMaster University; he also obtained a number of non-trivial extensions, but unfortunately mathemwticorum not seem too impressed withthem and never published his findings.

Let 5 be a closed, bounded, planeconvex set with the following property: He wanted to show, as is clear cdux his solution, how easy it is even fortrained people to arrive at the wrong answer sheep in this case by thought-lessly equating apples and oranges. Please use the online form to submit your digital material or scans of written material. Suppose there exists a convex polyhedron having exactly sevenedges.

Considerons maintenant deux cas: Arnold Summerfeld, Optics9 Academic Press, Descube; itwas published in [4] and I found it in [5], Note thatboth proofs given here were discovered by engineers andnot by professional mathematicians, which proves some-thing or other. The solution toFreidman’s proposal, which appeared in [4], is the one paraphrased above. For what value of I will it be able to graze overexactly half of the field? Macdonald High School; F.


CRUX: Information for Contributors and Authors

It is a far finer gambit than any chessgambit: Should you have any general questions or technical difficulties, please contact crux cms. Views Read Edit View history. This is the trap that our lone incorrect solverfell into. Then S is an ellipse. Thus there is no convex polyhedron having exactly seven edges.

After all that has been said about the internal angle bisector problem, onewould naturally expect the external angle bisectors to have the same property, namely: We thus have a contradiction.

Also solved by R. The Butterfly Problem has a history that goes back at least to [1],and the interest it arouses is such that it keeps on reappearing in the literature[]. Tidskrift, 2 3 – 1 ,pp. Les adresses sont done 88 et More generally, it is valid for every Pythagorean triangle threesides of integral length since every such triangle is similar to another inwhich the sides form a primitive Pythagorean triple, and it is well-knownthat, in all such triples a,b,ca and b are necessarily of different par-ity.