Varchas Koushik

"Pure mathematics is, in its way, the poetry of logical ideas." — Albert Einstein ⭐ What interests m...  
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Content Developer-Math

  • Byjus
  • Feb 2021 - Present

Consultant and Storyteller - Math

  • Get Set Rise Coaching and Consulting
  • Mar 2020 - Feb 2021
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Varchas 's Collections

Math stories

4 Highlights

Blog/Poetries

2 Highlights

Blog/Storytelling

1 Highlight

2021

Nov 27, 2021
Nov 27, 2021
Wrote a Blog Post
Published a story
Our story #4 revolves around the crime drama series ‘Numbers’. Numbers (stylized as NUMB3RS) follows FBI Special Agent Don Eppes and his brother Charlie Eppes, a college mathematics professor and prodigy, who helps Don solve crimes for the FBI.

The show #Numb3rs begins with:

“We all use math every day;
to predict weather, to tell time, to handle money.
Math is more than formulas or equations;
it's logic, it's rationality,
it's using your mind to solve the biggest mysteries we know.”
The series covers a host of math concepts over its 118 episodes. Let’s look at one of them briefly.

#Example1: 4th episode of the 4th season- ‘#Thirteen’.
Don and his team seem to be one step behind a killer who leaves numerological patterns in Bible verses at the scenes of his crimes.
In this episode, the killer is choosing his victims based on a system of beliefs rooted in numerology. Charlie is forced to learn about these beliefs, and determine what mathematical patterns the killer is using in order to predict the next victim.

#Trivia:
The title refers to the various beliefs surrounding the 'baker's dozen', up to and including triskaidekaphobia.
This appears at the beginning of the episode: "6 days of creation, 10 commandments, 14 stations of the cross, 1 Word of God" (Crazy, right?!)

A bit more into the episode:
When Professor Trowbridge is explaining various ways of looking at numbers, and portrays these as being too strange to be a coincidence, and implies that this is evidence for some higher meaning in the numbers.
Charlie replies by citing the "strong law of small numbers", which says that there are not enough small numbers to meet the many demands made of them.
This means that small numbers will often appear in more than one place, and so such things are much more likely to be coincidences than we would initially think.
Charlie says that "one will always find meaning where one seeks it".

#Math involved:
What is “strong law of small numbers”? (This is just one concept among the many used in the episode)

In mathematics, the "strong law of small numbers" is the humorous law that proclaims, in the words of #Richard .K. Guy (1988):
There aren't enough small numbers to meet the many demands made of them.
In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few.
Richard gives numerous simple, interesting and elegant examples for the same. (Don’t miss out reading a few examples in the document attached.)
The creators of the show use a variety of math concepts from Fibonacci sequence to complex statistical models, which makes the show highly entertaining for math enthusiasts.
Sources:
<1> Numb3rs TV series.
<2> Cornell Department of Mathematics- Numb3rs Math Activities.
<3> The Strong Law of Small Numbers by Richard .K. Guy- The American Mathematical Monthly.

#mathematics #numbers #story4
Nov 25, 2021
Nov 25, 2021
Published a story
Wrote a Blog Post
Practiced Storytelling
+ 1
My first experiences of storytelling kids is out here.
It answers the 'how' part in a simple 2 minute read :)

#storytelling #experiences #blog
Nov 24, 2021
Nov 24, 2021
Wrote a Blog Post
Published a story
In story#3 we are moving from ‘The Simpsons’ to its sister show ‘Futurama’ and their love for the number ‘#1729’.

From the starship’s registry number to a number of universe, 1729 appears in many episodes of Futurama.

#Some_titbits_about_1729:
1) 1729 is a Harshad number, a category of numbers discovered by the Indian Mathematician D.R. Kaprekar.
1 + 7 + 2 + 9 = 19, and 19 divides 1729. Also, 19 ✕ 91 = 1729 - a special type of Harshad’s number you see!
2) If we see the 1729th decimal place of ‘e’, then we see that it marks the start of the first consecutive occurrence of all ten digits in this famous irrational number.
3) 1729 is also the third Carmichael number, the first Chernick–Carmichael number, and the first absolute Euler pseudoprime. It is also a sphenic number.

#So_what’s_so_special_about_1729?
1729 has earned a special status due to one simple but elegant conversation between 2 greatest mathematicians of the 20th century Godfrey Harold Hardy, an English Mathematician and Srinivasa Ramanujan, arguably the greatest mathematical mind of the 20th century.
As per #Hardy,
“I remember once going to see him [Ramanujan] when he was lying ill at Putney, London. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways”, i.e.,
1729 = 1^3 + 12^3 = 9^3 + 10^3
Thus, 1729 came to be known as the #Ramanujan-Hardy number or in mathematical circles- the #taxicab_number.

#Fun_fact:
In one of the episodes, a taxicab’s number is 87,539,319. It is done because 87,539,319 is the smallest number that is the sum of cubes in three different ways, i.e.,
87,539,319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3
A fitting number for a taxicab isn’t it?
The writers of Futurama by referencing 1729 and 87,539,319, pay a fitting tribute to the greatest mathematical mind of 20th century #Srinivasa_Ramanujan.

<More fun facts in the comments section>

Sources:
<1> The Simpsons and their mathematical secrets written by Simon Singh.
<2> The Man Who Knew Infinity: A Life of the Genius Ramanujan - a biography on Srinivasa Ramanujan, written in 1991 by Robert Kanigel.
<3> Google images.

#thesimpsons #futrurama #taxicab #1729 #ramanujan #hardy #mathstories #story3
Nov 20, 2021
Nov 20, 2021
Published a story
Math story
Practiced Storytelling
+ 1
Remember the show that had predicted Donald Trump’s presidency?
Yes, Iam talking of #‘TheSimpsons’ in my story#2.

In the episode of “The Wizard of Evergreen Terrace” (1998),  Homer writes something on the blackboard.

#My_interest- the second equation on the board!
3987^12 + 4365^12 = 4472^12

#Why?
We all ID the equation: x^2 + y^2 = z^2,  right?!

Diophantus in his book 'Arithmetica', challenged his readers to find whole number solutions to the above equation. Well, there are infinite solutions to the equation.

#What’s_the_solution_for_the_above_equation?
Do #Pythagorean triples ring a bell?! (All the Pythagoras fans-Hifi!)

Okay, so what’s #special in #Homer’s_equation?
Homer seems to have defied Fermat’s last theorem!

Okay, now what’s #Fermat's last theorem?
Pierre de Fermat got bored of Diophantus’ puzzle of x^2 + y^2 = z^2.
He wanted to find solutions for x^3 + y^3 = z^3. He could just come up with trivial solutions like 0^3 + 7^3 = 7^3 and so on.
He further went on to raise the powers and tried to find solutions for them. Despite his best efforts he couldn't find any solution.
So, he concluded that it is impossible to find whole number solutions to any of the following equations:
x^3 + y^3 = z^3
x^4 + y^4 = z^4
      .
      .
      .
x^n + y^n = z^n, when n > 2.

He scribbled this in his copy of Diophantus’ Arithmetica in 1637.
He then confidently added this sentence (translated from Latin) “I have discovered a truly marvellous proof of this, which this margin is too narrow to contain” - most frustrating note in the history of mathematics, isn't it? 

#Is_Homer’s_equation_true?
Take your calculators and check it out NOW!
If you have a calculator that can show more than 8 digits, then you’ll realise that it's not exactly correct, but almost!

The actual equation is:
3987^12 + 4365^12 = 4472.0000000070576171875^12

Well, Fermat’s theorem still holds good (and the 130 page proof given by Andrew Wiles too!)

This was a #mathematical_prank played by the writer David .S. Cohen!!
Cohen obviously knew Fermat’s equation had no solutions but this way he paid homage to one of the greatest mathematical minds Fermat and, also to Andrew Wiles. The prank amused almost everybody who were aware of Fermat's last theorem and checked out the same with the calculator.

#How_did_Cohen_find_Homer’s_equation?
In order to find this pseudo-solution, he wrote a computer program that would scan through the values of the variables involved until it found a number that was almost balanced. Wow! Isn’t it?
More about the author in the comments section.

The Simpsons has a lot of mathematical tit bits in its episodes! Hopefully I will cover few of the most intriguing ones through my posts.

Stay tuned for more stories on math!

Sources:
<1> The Simpsons and their mathematical secrets - a wonderful book written by Simon Singh.     (For all math lovers- give it a read! You’ll have fun!)
<2> Google images.

#thesimpsons #fermat #homer #mathstories #theorems
Nov 17, 2021
Nov 17, 2021
Published a story
Wrote a Blog Post
Wrote A Poem
+ 1
Just published my 2nd poem "Thank you note to my dearest mother :)" on medium.
Check it out here

#poem #mother #thankyou #gratitude #influence #blog
Nov 14, 2021
Nov 14, 2021
Wrote a Blog Post
Wrote A Poem
#poem #blog #1

Toast to a new beginning- 2021

Link to the poem - here.
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