Problem of the Week 12-27-18: What is b? [Algebra]

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Problem of the Week 12-20-18: Find the Square's Area [Geometry]

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Bogus Proofs

This series explores common mathematical fallacies. Each proof consists of steps that are seemingly correct, but there is an error in each argument that leads to some absurd result. 

Warning: You may be convinced by these proofs, and your common sense may be threatened.

Can you spot the mistakes? 

1.

 2.

 3.

4.

5.

6. 

7.

8. 

To find out where each proof went wrong, check out our video series: 

We hope you had as much fun with this series as we did! If you have any cool bogus proofs, be sure to share them with us on social media.

Problem of the Week: 12:13-18: Taylor Series Approximation and Remainder Estimation [Calculus]

Today is Taylor Swift's birthday.

Surely, we had to take this opportunity to do a problem that involves a Taylor series.

Side note: Taylor series was formulated by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor . 

We have no idea what T-Swizzle's background in mathematics is.

Solution:

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Problem of the Week: 12-06-18: Math Test [Combinatorics]

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Problem of the Week: 11-29-18: Find their Birthdays [Algebra]

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Sorry guys, the woman was born in 1983 not 1973. I'm still living in 2008. The solution above is correct,

Problem of the Week: 11-21-18 Thanksgiving Banquet

Happy Thanksgiving!

Solution:

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Edit: At 2:25, the inequality is between five hundred and *SIX HUNDRED* not 16 :)

Problem of the Week 11-15-18: Harry Potter Currency [Arithmetic]

Tomorrow marks 17 years since Harry Potter and the Sorcerer's Stone was released in theaters.

Obviously we needed to do a Harry Potter themed Problem of the Week. 

 Does Hogwarts teach math? 

Solution

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Problem of the Week: 11-08-18: Prove Pasch’s Postulate as a Theorem [Geometry]

Happy 175th birthday Moritz Pasch! The German mathematician was born on November 8, 1843. Pasch specialized in the foundations of geometry. He is best remembered for Pasch's axiom, which he discovered in 1882. 


Although axioms do not require proofs, in this week's problem we celebrate Pasch's birthday by- you guessed it- proving Pasch's axiom. Why? Because proofs are FUN.     

Solution:

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Problem of the Week: 11-01-18: Election Exit Polls [Probability]

Midterm elections are just around the corner. Don't forget to go out and VOTE! In the meantime, give this election-edition problem a try!

Solution 

Video

Problem of the Week: 10-25-18: Halloween Monster Party [Logic Puzzle]

Halloween is less than a week away! Celebrate early with this Halloween themed Problem of the Week. 

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Solution:

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Problem of the Week: 10-18-18: Prove that the Fraction is Irreducible [Number Theory]

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Problem of the Week: 10-11-18: Baseball Bet [Probability]

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Solution

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Problem of the Week: 10-04-18: Arc Length [Calculus]

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Solution

Video

Problem of the Week: 09-27-18: Comparing Numbers [Inequalities]

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Solution

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Problem of the Week: 09-20-18: Separation of Variables [Differential Equations]

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Problem of the Week: 09-13-18: Two Independent Events [Probability]

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Problem of the Week: 09-06-18: Solving Linear Congruence using Fermat's Little Theorem [Number Theory]

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Problem of the Week 08-30-18: Solving Equation for Variables [Algebra]

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Problem of the Week 08-23-18: Solving a Trigonometric Equation [Trig]

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Problem of the Week 08-16-18: Nullspace of a Matrix [Linear Algebra]

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Problem of the Week 08-09-18: Logarithmic Differentiation [Calculus]

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Problem of the Week 8-02-18: Double Integral [Calculus]

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Solution below:

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*Edit: there is not suppose to be a constant of integration at the end since this is a definite integral.

The Fields Medal

Today, Peter Scholze, Caucher Birkar, Alessio Figalli, and Akshay Venkates won the Fields Medal- the highest honor a mathematician can receive. 

To celebrate their victory, we compiled a list of important facts about the award:

1. The Fields Medal is awarded to two, three, or four mathematicians under the age of 40.

The Fields Medal

2. It has been awarded every four years since 1950 at the International Congress of Mathematicians. 

3. The award “recognizes outstanding mathematical achievement for existing work and for the promise of future achievement.” 

4. An individual cannot win a Fields Medal more than once.

5. Many describe the Fields Medal as the mathematician's "Nobel Prize."

6. There is a monetary award of about $15,000 Canadian dollars.

7. The award is named after Canadian mathematician John Charles Fields.

John Charles Fields

8. Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas were the first recipients in 1936.

9. Maryam Mirzakhani became the first woman to win the Fields Medal in 2014

10. Jean-Pierre Serre became the youngest recipient at the age of 27. 

11. In 2006, Grigori Perelman, refused his Fields Medal. He said, "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo.”

12. So far, 4 mathematicians under the age of 30 have won.

Source: 

Wikipedia 

Problem of the Week 7-26-18: 2nd Order Nonhomogenous Linear Differential Equation [Differential Equations]

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Problem of the Week 7-19-18: Invertible Matrix [Linear Algebra]

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*Note: In the video, k² - 1 - 6(k - 1) reduces to k²- 6k + 5 NOT k² - 6k - 5

Unlucky Numbers Around the World

via GIPHY

Friday the 13^th is upon us!  Across the nation, there are people avoiding black cats, spilled salt, ladders, and broken mirrors. Not everyone, however, is scared of 13 because they have other numbers to fear. 

In honor of today, here are 6 unlucky numbers from around the world.

4 - China

In China, the number 4 is considered unlucky because it is homophonous to the word "death." Similar to how the 13^th floor is absent in many buildings in the West, the 4^th floor is often left out in China.

9 - Japan

Just like the number 4 in China, the number 9 is a bad omen in Japan because it sounds similar to the Japanese word for “torture.”

17 - Italy

The Roman numeral for 17 is XVII, and an anagram for XVII is "VIXI.” This translates to “I lived," aka “my life is over."

26  - India 

For India, tragedies and disasters have the pattern of striking on the 26^th (the 2008 Mumbai terror attack, the 2001 Gujarat earthquake, the 2004 Indian Ocean tsunami, 2008 Ahmedabad bomb blasts). For this reason, India doesn't really like the number 26. Can you blame them?

39 - Afghanistan

The number 39 is considered cursed in Afghanistan due to the fact that 39 translates to  ‘morda gow’ which means ‘dead cow” - which is slang for pimp. Since 39 is linked to prostitution, the number is largely avoided.


0888 888 888 - Bulgaria
After three people in Bulgaria with the phone number 0888 888 888 died within ten years, a Bulgarian mobile company suspended the phone number because they believed it was cursed. If you are in Bulgaria, try calling the number. Surely, no one will pick up. 

If we missed any unlucky numbers in your culture, be sure to comment below. Also, be sure to check out past blog posts about Friday the 13th. 
1. 13 Facts about the Number 13
2. Friday The 13th, Math and Music.

Sources:

https://news.nationalgeographic.com/news/2013/09/130913-friday-luck-lucky-superstition-13/

http://www.smosh.com/articles/unlucky-numbers-different-cultures-around-world

https://listverse.com/2015/03/06/10-numbers-that-launched-absurd-superstitions/