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Mouhammad Fakhoury
Works at Business Empower
Attended Syracuse University
Lived in Seattle, WA
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Mouhammad Fakhoury

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Mouhammad Fakhoury

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Looking for a jet-lag cure? A new mathematical model may help you overcome jet lag faster than anyone thought possible.
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#Ketwket is the first app based on #Nodejs technology coming to you from #Adsia
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Very promising!  I would invest in this one :) 

#PencilCase
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Mouhammad Fakhoury

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Spherical zillij

This beautiful golden pattern was created by someone who goes by the name of Taffgoch.  He did it by taking a traditional Islamic tiling pattern made of interlocking hexagons and replacing some of them by pentagons.  This lets the original flat pattern 'curl up' and become spherical!

You can see the original flat pattern here:

https://groups.google.com/d/msg/geodesichelp/ayZcCILttBs/bVU6eI5SLUEJ

It's of a type called zillij.   It's fun to read how Taffgoch transformed it into the round version... and see how he improved it step by step.

Puzzle: how many pentagons, and how many hexagons, are in this spherical zillij?

This is similar to a question about fullerenes, which are sheets of graphite - hexagons of carbon - that curl up into spheres because some hexagons are replaced by pentagons.  Fullerenes come in different sizes, with different numbers of hexagons.  But as long as a fullerene is spherical in its topology, with 3 pentagons or hexagons meeting at each corner, the number of pentagons is fixed!  

I'll compute this number now, so if you want to answer the puzzle on your own, maybe you should stop reading.  However, this spherical zillij pattern is not exactly the same as a fullerene... so it's not obvious that it has the same number of pentagons.

Here's how it goes.  Suppose we have a sphere tiled with P pentagons and H hexagons, with 3 of these polygons meeting at each vertex.

How many edges are there in this tiling?  Each pentagon has 5 edges, and each hexagon has 6, but each edge is shared by 2 shapes so the number of edges is

E = (5P + 6H)/2

How many vertices are there?  This is where we need to know 3 polygons meet at each vertex.  Then by the same reasoning as above, the number of vertices is

V = (5P + 6H)/3

How many faces are there?  That's easy:

F = P + H

Now Euler's formula, a fact from topology, says

V  -  E  +  F = 2

So, plugging in the equations for V, E, F, we get

(5P + 6H)/3  -  (5P + 6H)/2  +  (P + H) = 2

or

P + H = 2  +  (5P + 6H)/6

or

P = 12

Note that H cancels out, so we learn nothing about how many hexagons there are.  But pentagons love the number 12... and ultimately, that's why this shape here has

5 × 12 = 60

rotational symmetries!

Puzzle: suppose we have a doughnut with g holes tiled by pentagons and hexagons, 3 meeting at each corner.  How many pentagons are there?

#geometry  
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Positive Intelligence, looks like a great book to read.
http://amzn.com/B007R0IQ70
 
Stanford Professor Shirzad Chamine is author of the New York Times bestseller Positive Intelligence. His work exposes 10 well-disguised mental saboteurs and shares how to defeat them. According to Chamine, "positive intelligence" measures the percentage of time our mind serves us as opposed to sabotaging us. 
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4 reasons Microsoft is a new company.

Microsoft is a new company. While it's true that many of the changes announced under the leadership of CEO Satya Nadella were initiated under his predecessor, Steve Ballmer, it's still clear that this isn't the same old company: It's barbecuing sacred cows and embracing smart new directions.

Here are four surprising things Microsoft has embraced publicly in the past week or so that reveal a new and better company.

http://www.computerworld.com/s/article/9247446/4_reasons_Microsoft_is_a_new_company

#Microsoft   #satyanadella  
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Very funny and typical!
 
Hahaha! Great sketch.
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Why would the discovery of gravitational waves from the early Universe be such a big deal?  To get a sense of this, take a walk back in time to when these waves would have been formed:

380 thousand years after the Big Bang - recombination.  Hydrogen gas cools down to form molecules.  The universe becomes transparent, and light from the hot gas moves freely through it, eventually becoming the cosmic background radiation we see today.
Temperature: 3000 Kelvin.

10 thousand years after the Big Bang - end of the radiation-dominated era.   At this point more energy is in the form of matter than in the form of light. 
Temperature: 12,000 Kelvin.

1000 seconds after the Big Bang - decay of lone neutrons.  There had been lots of lone protons, neutrons and electrons.  But a neutron by itself is unstable: it decays into a proton, an electron and an anti-electron neutrino.  The protons and electrons will later form hydrogen. 
Temperature: roughly 500 million Kelvin. 

180 seconds after the Big Bang - beginning of nucleosynthesis.
Some neutrons stick to protons, forming nuclei of heavy hydrogen, helium, and a tiny bit of other stuff. 
Temperature: roughly 1 billion Kelvin.

10 seconds after the Big Bang - annihilation of electron-positron pairs.   At high enough temperatures, photons in the intense form of light called gamma rays can collide and form electrons and their antiparticles, called positrons.  Now the universe cooled down to the point where this ceased: most electron-positron pairs annihilated and turned into light, leaving a tiny excess of electrons. 
Temperature: roughly 5 billion Kelvin.

1 second after the Big Bang - decoupling of neutrinos.  At high enough temperatures, neutrinos are so energetic that they interact a lot with other particles.   But now the universe cooled to the point where this stopped. 
Temperature: roughly 10 billion Kelvin.

100 microseconds after the Big Bang - annihilation of pions.  At high enough temperatures colliding particles have enough energy to make pions, one of the lightest particles after electrons.   Now the universe cooled to the point where this stopped and the pions, being unstable, decayed. 
Temperature: roughly 1 trillion Kelvin.

50 microseconds after the Big Bang - QCD phase transition. At high enough temperatures quarks can roam freely.  At this point the universe cooled enough that the quarks became bound by the strong nuclear force into little blobs called neutrons and protons.
Temperature: 1.7-2.1 trillion Kelvin

10 picoseconds after the Big Bang - electroweak phase transition. At this point, the electromagnetic and weak nuclear force became different, thanks to their interactions with the Higgs boson.  At higher temperatures they were indistinguishable. 
Temperature: 1-2 quadrillion Kelvin.

So far, we've gone back to 10^{-11} seconds after the Big Bang - 10 trillionths of a second!  I feel our understanding of the early Universe is fairly solid back to this time, because we've done experiments to understand physics up to the temperatures that prevailed then.  For example, we're pretty sure the Higgs boson is real.

Further back, things get more mystderious.  But the new BICEP2 experiment seems to be shedding light on the 'inflationary era' roughly 10^{-35} seconds after the Big Bang!  

For more details, I think +Sean Carroll's blog is good:

http://www.preposterousuniverse.com/blog/2014/03/16/gravitational-waves-in-the-cosmic-microwave-background

For more on why physicists aren't completely convinced by the new results, try +Philip Gibbs's blog:

http://blog.vixra.org/2014/03/20/how-certain-are-the-bicep2-findings/

Briefly: some of the BICEP2 results are very different from the Planck experiment, and the Planck folks are going to look into this.  And of course, there's probably a lot of unknown physics between the energies and temperatures we can probe in colliders here on Earth and those that prevailed 10^{-35} seconds after the Big Bang! 

But we're making good progress.

  #astronomy
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SUPERB VIDEO Where PETER DIAMANDIS Explains With Crystal Clear Clarity The FANTASTIC NEAR FUTURE That Is WAITING FOR US And Whose "Seeds" Exist Right Now.

The World in 2050
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Have him in circles
284 people
Steven Miles's profile photo
Mouhammad Fakhoury's profile photo
Khalil Dandan's profile photo
Lauren Weinstein's profile photo
Rawad Hani's profile photo
Work
Occupation
Computer Science
Employment
  • Business Empower
    CEO, 2008 - present
  • Microsoft Corporation
    Principle Software Engineer, 1997 - 2008
  • Adobe Systems
    Computer Scientist, 1992 - 1997
  • Aldus Corporation
    Principle Architect, 1990 - 1992
  • Silicon Beach Software
    Software Developer, 1990 - 1992
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Previously
Seattle, WA - San Diego, CA - Scarsdale, NY - Syracuse, NY - Bellevue, WA - Beirut
Story
Bragging rights
Here are some of the cool products I helped develop: Aldus Intellidraw (precursor to Flash with Jonathan Gay and Robert Tatsumi), Aldus PageMaker, Adobe Indesign, Microsoft PictureIt, Microsoft Greetings Workshop,Digital Imaging Suite, MSN, Windows Server, Windows, Windows Live
Education
  • Syracuse University
    Electrical and Computer Engineering, 1979 - 1987
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Male