## Profile

## Stream

### Mohammed S. Al Sahaf

Shared publicly -### Mohammed S. Al Sahaf

Shared publicly -### Mohammed S. Al Sahaf

Shared publicly -### Mohammed S. Al Sahaf

Shared publicly -### Mohammed S. Al Sahaf

Shared publicly -*"The Islamic State (IS) group says it was behind a suicide bombing on a Shia mosque in Saudi Arabia that killed at least 21 people.*

*The attack in Saudi Arabia's Eastern Province is the first to be claimed by the Saudi branch of IS, which was formally established last November."*

### Mohammed S. Al Sahaf

Shared publicly -*"We found measles predisposes children to all other infectious diseases for up to a few years," Mina says.*

#scienceeveryday

### Mohammed S. Al Sahaf

Shared publicly -**Why is this true?**

The spooky-smart mathematician Srinivasa Ramanujan came up with this formula around 1913. Why is it true?

I don't know, let's see...

In 1735, a young fellow named Euler stunned the world by cracking a famous puzzle that had been unsolved for almost a century: the

**Basel problem**. The problem was to sum the reciprocals of perfect squares:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... = ???

Euler showed that the answer was π²/6:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... = π²/6

He also showed you could rewrite this sum as a product over primes:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... =

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ...

That's actually the easy part: it's a cute trick called the

**Euler product formula**.

So we know

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ... = π²/6

If you think about it, Ramanujan's formula is saying that

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ...

is 2/5 as big. So, proving it is the same as showing

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... = π²/15

Maybe the next step is to use the same idea as the Euler product formula. I think this gives

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... =

1/1² - 1/2² - 1/3² + 1/4² + 1/5² - 1/6² + 1/7² + ...

where the signs at right follow a fancy pattern: we get 1/n² whenever n is the product of an

*even*number of primes, and -1/n² when n is the product of an

*odd*number of primes. For example, 4 = 2 x 2 is the product of an even number of primes, so we get 1/4².

So I'm left wanting to know why this strange sum

1/1² - 1/2² - 1/3² + 1/4² + 1/5² - 1/6² + 1/7² + ...

equals π²/15. Ramanujan, dead since 1920, is still messing with my mind!

The formula is supposed to be in here:

• Srinivasa Ramanujan, Modular equations and approximations to π,

*Quart. J. Pure. Appl. Math.*

**45**(1913-1914), 350-372. Also available at ://ramanujan.sirinudi.org/Volumes/published/ram06.pdf.

But I don't see it!

Here you can see how Euler solved the Basel problem:

https://en.wikipedia.org/wiki/Basel_problem

It's a great example of his brilliant tactics, many of which were far from rigorous by today's standards... but can be made rigorous.

#mathematics

### Mohammed S. Al Sahaf

Shared publicly -### Mohammed S. Al Sahaf

Shared publicly -*The Machine That Made Us is a documentary in which Stephen Fry examines the story behind the first media entrepreneur, printing press inventor Johann Gutenberg, to find out why he did it and how, a story which involves both historical inquiry and hands-on craft and technology.*

*Fry travels across Europe to find out how Gutenberg kept his development work secret, about the role of avaricious investors and unscrupulous competitors and why Gutenberg's approach started a cultural revolution. He then sets about building a copy of Gutenberg's press.*

#fryday #Gutenberg

- Saad Specialist HospitalWeb Developer, 2014 - present
- CourseraVolunteer Translator, 2012 - present
- TEDVolunteer Translator, 2011 - present
- Khan AcademyVolunteer Translator, 2011 - present
- University of TulsaJava Tutor, 2011 - 2011
- University of TulsaMATLAB Tutor, 2011 - 2011

- Amazon Wishlist (current)
- My WordPress Blog - Check it out! (current)

TextSecure Private Messenger - App Android su Google Play market.android.com TextSecure is a messaging app that allows you to take back your privacy while easily communicating with friends.Using TextSecure, you can co |

How Apple and Amazon Security Flaws Led to My Epic Hacking | Gadget Lab ... www.wired.com In the space of one hour, my entire digital life was destroyed. First my Google account was taken over, then deleted. Next my Twitter accoun |

Game Theory www.game-theory-class.org Game Theory is a free online class taught by Matthew Jackson and Yoav Shoham. |

47 Mind-Blowing Psychology-Proven Facts You Should Know About Yourself www.businessinsider.com You can't actually multitask, you're more susceptible to ads when you're sad, and other surprising facts. |

HowStuffWorks "10 Scientific Laws and Theories You Really Should Know" science.howstuffworks.com 10 scientific laws and theories you should know are explained in this article from HowStuffWorks. Learn about 10 scientific laws and theorie |

Abandoning Algebra Is Not the Answer | Observations, Scientific American... www.scientificamerican.com In an opinion piece for the New York Times on Sunday, political science professor Andrew Hacker asks, |

The Fabric of the Cosmos: What Is Space? www.youtube.com Surprising clues indicate that space is very much something and not nothing. The Fabric of the Cosmos Acclaimed physicist Brian Greene revea |

The Danger of Using Tests to Measure Success - Education - GOOD goo.gl A school board member's testing philosophy changed after he took the standardized tests for his district's 10th graders—and did miserably. |

Discovering Electromagnetism | Daylight Atheism | Big Think feedproxy.google.com In Carl Sagan's The Demon-Haunted World, there's a chapter titled "Maxwell and the Nerds" about James Clerk Maxwell, the S |

WHY HARD: Why Electricity is Impossible to Understand amasci.com BELOW are my original 1989 notes and "raw data" for finished articles on Amasci.com. Why are my explanations different than usual? Because t |

Think with Google - Your resource for industry trends & insights www.thinkwithgoogle.com Think with Google brings together industry trends, insights, and research from the most compelling thought leaders, marketers, and academics |

Dan Ariely | Professor of Behavioral Economics, Duke University | Big Think bigthink.com Full Interview, 39:14, Discuss. Why Online Dating Is So Unsatisfying, 7:40, Discuss. Who You Find Attractive Is Based on How Hot You Are, 6: |

Decisions Are Emotional, not Logical: The Neuroscience behind Decision M... bigthink.com Think of a situation where you had bulletproof facts, reason, and logic on your side, and believed there was absolutely no way the other per |

Can Nano Breakthrough Revolutionize Solar Power? | IdeaFeed | Big Think bigthink.com What's the Latest Development? A new way to extract electrical current from semiconductors may revolutionize solar power, finally making pho |

The Right Mindset | Moments of Genius | Big Think bigthink.com “Are great musician born or made?” That question was posed by Gary Marcus, who at the age of 38, wondered if he could overcome a lifetime of |

Approaching Normal | World in Mind | Big Think bigthink.com Nearly two decades ago, I walked into my first Abnormal Psychology class. Given the course title, I thought I had a pretty good handle on wh |

Dr. Michio Kaku's Playlist: Five Science Videos You Must See | Big Think... bigthink.com What is the meaning of infinity? How can the Higgs boson be explained in a way that is clear and accessible? The answers to these questions |

The Flaws in Defending Morality With Religion | Against the New Taboo | ... bigthink.com When we think of those opposed to homosexuality – which still sounds weird to me, like opposing left-handed people* – or stem-cell research |