Posted in Algebra, Beautiful math, Simple math by: admin

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24 Feb

TweetIn a recent blog A Lovely Observation Gary Davis (@RepublicOfMath) elaborated on an observation of Ben Vitale (@BenVitale) to the effect that In the fractions both numerators and denominators are sums of successive odd numbers: the numerators start with 1, the denominators where the numerators leave off. Thus naturally derivation of the formula for the […]

Posted in About math, Books to read, Curiosity, Uncategorized, Wisdom to live by by: admin

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21 Feb

TweetThe bible takes six words to describe the evolution of the Hebrew tribe in Egypt from 70 souls to a people (Exodus 1.7). The closest translation I found among several is this: "... and the sons of Israel have been fruitful, and they teem, and multiply, and are very very mighty ..." In Hebrew, the […]

Posted in A must see, Algebra, Arithmetic, Beautiful curiosity, Curiosity, math fun by: admin

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20 Feb

TweetFor a prime , two integers are both divisible by with the probability , because this only happens when the two integers have the residue 0 (one out of available residues) modulo . Two integers are mutually prime if they have no common nontrivial factors, prime facors in particular. Assuming divisibility by one prime is […]

Posted in Curiosity, Education reform, Uncategorized by: admin

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20 Feb

TweetI've been following up on a story according to which George Dantzig - the father of linear programming - once happened to be late to a lecture. When he arrived, he copied down from the blackboard two problems he thought to be a homework assignment. He solved them at home not knowing that the two […]

Posted in Homeschooling, math fun, Simple math by: admin

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19 Feb

TweetHere are a few engaging problems that many a student will be able to solve and, if not, would be able to appreciate the simplicity of a missed solution. Without a measuring tape, is it possible to cut a half-meter piece from the rope of 2/3 m length? Solution What is the digital root of […]

Posted in geometry, Homeschooling, Simple math by: admin

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01 Feb

TweetThe three angle bisectors of a triangle meet at incenter of the triangle. Reversing the problem we may ask a relevant question: Given three concurrent lines: α, β, and γ. Is there always a triangle with the three lines as the angle bisectors. If so, construct the triangle. Solution Given three concurrent lines: α, β, […]

Posted in geometry, Homeschooling, Simple math by: admin

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01 Feb

TweetThe medians of a triangle meet at a point known at the center of the triangle. Reversing the problem we may ask a relevant question: Given three concurrent lines: α, β, and γ. Is there always a triangle with the three lines as the medians. If so, construct the triangle. Solution Given three concurrent lines: […]