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Alexander Bogomolny
Works at CTK Software
Attended Moscow State University
Lives in NJ, USA
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Alexander Bogomolny

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A curious property of number 4: 4 = k^2 - (k+1)^2 - (k+2)^2 + (k+3)^2 and what follows from it

http://www.cut-the-knot.org/arithmetic/algebra/PropertyOfNumber4.shtml
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Alexander Bogomolny

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On a simple closed curve there exist 3 points that are vertices of an equilateral Δ

www.cut-the-knot.org/m/Geometry/EquilateralTriangleOnCurve.shtml
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Alexander Bogomolny

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My review of Single Digits by Marc Chamberland

http://www.cut-the-knot.org/books/Reviews/SingleDigits.shtml
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Alexander Bogomolny

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Up and down
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A curious configuration of isosceles triangles in a triangle: At vertices of a triangle construct three similar isosceles triangles with bases on opposite sides.The six sides of these three similar isosceles triangles intersect each other at six concyclic points.

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

There are also concyclic quintuplets and quadruplets.
The sides of three isosceles triang;es cross at six concyclic points
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Fantastic 
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Alexander Bogomolny

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Two trigonometric proofs of the Pythagorean theorem based on the half-angle formulas

http://www.cut-the-knot.org/pythagoras/Proof109.shtml
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Alexander Bogomolny

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A small rectangle cut off a bigger one, draw a line that halves the area of that shape

http://www.cut-the-knot.org/m/Geometry/CutInHalf.shtml 
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Strange lighting just before a snowstorm (3/1/2015)

#birdphotography  
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Thank you so much

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Alexander Bogomolny

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Proof 111 of the Pythagorean theorem - via analytic geometry http://www.cut-the-knot.org/pythagoras/Proof111.shtml
Pythagorean Theorem by Analytic Geometry: another trigonometric proof of the Pythagorean theorem
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A case of spontaneous synchronization
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Alexander Bogomolny

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Most of the time everything goes according to a plan, but sometimes the plan just does not make any sense, and sometimes someone just screws up.

http://www.odometer.com/lifestyle/9137/23-road-construction-fails-completely-lacking-common-sense#slide/0 
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It's near the end...the Pamida parking lot!
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An outgrowth of the concurrencies noted earlier in the Hofstadter configuration
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People
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
Story
Tagline
Love math. Care for math education.
Education
  • Moscow State University
    MS Mathematics, 1966 - 1971
  • Hebrew University of Jerusalem
    PhD Mathematics, 1976 - 1981
Basic Information
Gender
Male