### Alexander Bogomolny

Shared publicly -You may think they are kissing. On close inspection, though, I believe they just gossip.

#birdphotography #naturephotography

#birdphotography #naturephotography

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Alexander Bogomolny

Works at CTK Software

Attended Moscow State University

Lives in NJ, USA

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You may think they are kissing. On close inspection, though, I believe they just gossip.

#birdphotography #naturephotography

#birdphotography #naturephotography

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The set of numbers 1,...,2N is split into two, A={a_i} and B={b_i} of N elements each. Elements of one are arranged in the increasing order, those of the other in decreasing order. Here's an elegant geometric proof that Σ|a_i - b_i| = N²

http://www.cut-the-knot.org/wiki-math/index.php?n=Arithmetic.GeometricProizvolov

http://www.cut-the-knot.org/wiki-math/index.php?n=Arithmetic.GeometricProizvolov

Stuart Anderson. As in the description at another page consider the numbers A = \{a_1,\cdots,a_N\} chosen from S = \{1,\cdots, 2N\}, and the set complement B = S\setminus A = \{b_1,\cdots,b_N\}. Let the a_i be arranged in ascending order and the b_i in descending order.

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How to construct a regular hexagon from an arbitrary one. Here's one way. http://www.cut-the-knot.org/m/Geometry/DaoBarlottiSix.shtml

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On a morning stroll, I saw a starling fly into a tree hole. It took some patience, but 15 or so minutes later the bird peeped out with what appeared to be a small piece of wire that had no place in a nest. The temperature was 40F. While waiting for the bird to show itself I was longing to get a whiff of the global warming.

#birdphotography #naturephotography

#birdphotography #naturephotography

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Given three squares BCDE, ABIF, and ACJG, the latter two with centers O and O'. Let P be the midpoint of DG, N that of EF, S the intersection of NO' and OP. Then AS passes through M, the midpoint of DE

http://www.cut-the-knot.org/m/Geometry/ThreeSquares.shtml

http://www.cut-the-knot.org/m/Geometry/ThreeSquares.shtml

Given three squares BCDE, ABIF, and ACJG, the latter two with centers O and O'. Let P be the midpoint of DG, N that of EF, S the intersection of NO' and OP. Then AS passes through M, the midpoint of DE

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In his circles

47 people

Eastern kingbird.

On a branch it looks royal, but when in flight, it was catching flies as the next fellow.

#birdphotography #naturephotography

On a branch it looks royal, but when in flight, it was catching flies as the next fellow.

#birdphotography #naturephotography

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A common grackle. Judging by its apparent concentration, if it had a camera it would have reciprocated with my mug photo.

#birdphotography #naturephotography

#birdphotography #naturephotography

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An unusual case when six equilateral triangles yield a regular hexagon.

Let BED,HIF, DLJ,FGA, ACB,JKH be six equilateral triangles such that BED=HIF, DLJ=FGA, ACB=JKH and AF+BD=AB. Then GCELKI is a regular hexagon and its area equals 3\sqrt{3}/4(AF^2+AB^2+BD^2).

http://www.cut-the-knot.org/m/Geometry/HexagonFromNothing.shtml

Let BED,HIF, DLJ,FGA, ACB,JKH be six equilateral triangles such that BED=HIF, DLJ=FGA, ACB=JKH and AF+BD=AB. Then GCELKI is a regular hexagon and its area equals 3\sqrt{3}/4(AF^2+AB^2+BD^2).

http://www.cut-the-knot.org/m/Geometry/HexagonFromNothing.shtml

Let BED,HIF, DLJ,FGA, ACB,JKH be six equilateral triangles such that BED=HIF, DLJ=FGA, ACB=JKH and AF+BD=AB. Then GCELKI is a regular hexagon and 3\sqrt{3}/4(AF^2+AB^2+BD^2)

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People

In his circles

47 people

Communities

5 communities

Education

- Moscow State UniversityMS Mathematics, 1966 - 1971
- Hebrew University of JerusalemPhD Mathematics, 1976 - 1981

Basic Information

Gender

Male

Story

Tagline

Love math. Care for math education.

Work

Occupation

Software and web dvelopment, most happily math related

Skills

Mathematics - applied and otherwise, programming Java and C++

Employment

- CTK SoftwarePrincipal, present

Places

Currently

NJ, USA

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YouTube

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