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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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http://www.cut-the-knot.org/do_you_know/GoldenPentacross.shtml

An unanswered question: what area is covered with such tessellation?
A construction of the The Golden Pentacross and the tessellation of the plane
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Alexander Bogomolny

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Done 💪
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Alexander Bogomolny

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Golden Ratio in a Butterfly Astride an Equilateral Triangle

http://www.cut-the-knot.org/do_you_know/GoldenRatioAstrideEquilateralTriangle.shtml
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Another inequailty for points on the incircle - a problem for juniors

http://www.cut-the-knot.org/triangle/PointsOnIncircleAnotherLook.shtml
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Yet another condition for a triangle to be equilateral

http://www.cut-the-knot.org/m/Geometry/IncircleInEquilateralTriangle.shtml
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Alexander Bogomolny

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Lines AD,CB,CD are tangent to a given circle at A, B, and N, respectively. M is the midpoint of the arc AB opposite N; P=AB\cap DM, Q=AB\cap CM. Prove that PQ=AP+BQ.
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The necessary and sufficient condition for Hlawka's inequality to become equality

http://www.cut-the-knot.org/wiki-math/index.php?n=Geometry.QuadrilateralInequality
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Product-to-sum formulas for sine and cosine, a PWW

http://www.cut-the-knot.org/triangle/SinCosFormula4.shtml
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Three inequalities from Vietnam in six parameters linked by a matrix equation

http://www.cut-the-knot.org/m/Algebra/ThreeJPfromVietnam.shtml
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Alexander Bogomolny

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f'(x)=f'(1-x) on [0,1]. Prove that int(f,0,1) is not less than sqrt(f(0)f(1))
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Alexander Bogomolny

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A result whose corollary is a generalization of the previous post concerning circles centered at the incenter of a triangle. (With appreciation to +Snail Erato)

http://www.cut-the-knot.org/triangle/CirclesInBarycentricCoordinates.shtml
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Alexander's Collections
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