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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   
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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
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
From Arbitrary Hexagon to Regular One
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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  
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Alexander Bogomolny

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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
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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A cormorant drying up on a pond shore

#birdphotography   #naturephotography   #cormorant  
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Red-bellied woodpecker

#birdphotography   #naturephotography   #woodpecker  
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Eastern kingbird. 

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  
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Enjoying a sunset

#naturephotography   #sunsetphotography  
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Alexander Bogomolny

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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 3\sqrt{3}/4(AF^2+AB^2+BD^2)
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A drinking sea lion. #newyorkcity   #Zoo.
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People
Education
  • Moscow State University
    MS Mathematics, 1966 - 1971
  • Hebrew University of Jerusalem
    PhD 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 Software
    Principal, present
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
NJ, USA