Back to School – Friendship Math

Group Of Children Sitting On Bench In Mall

It is the first day of a new school year, and this class has only 10 students.  Ashley has 9 friends, Betty has 8, Caleb has 7, Derek has 6, Elaine has 5, Graham has 4, Henri has 3, Ivana has 2, Julie has 1.  Name one of Fred’s friends.

Answer

friends4In a group of 4 school children, each child has exactly two friends, just one of which is their best friend. What is the minimum possible number of children for whom their best friend is also that friend’s best friend?

Answer

 

It is the first day of a new school year, and this class has only 10 students.  Ashley has 9 friends, Betty has 8, Caleb has 7, Derek has 6, Elaine has 5, Graham has 4, Henri has 3, Ivana has 2, Julie has 1.  How many friends does Fred have?

Answer

It is the first day of a new school year, and this class has only 5 students. Amy has no friends yet. Betty has one friend. Chris has three friends. Derek has two friends.  How many friends does Ellie have?

Answer

In a group of five students, Ann has one real friend among them, Betty has two,  Craig has three, and Dianna has two. How many real friends does Edgar have in the group?

Answer

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Math Symbols

We use math symbols to express complex mathematical texts in a shorter form.

=   replaces   “is equal to

+ replaces “and

×   replaces   “multiplied by

. . . .

There are many Greek symbols like   π ∑   and special symbols like   √ ∞ ∈   in mathematics.

John David Walters explains where math symbols come from in the video:

Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

subwaymap2

Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

 

 

The perfect explanation is given in the PBS Infinite Series video:

Follow Your Passion in Math

Grow your passion by motivating practice like the 11-year-old Math Marvel

“Chess is a mathematical poem” – Aarushi Maheshwari 

Mathematical Beauty

e + 1 = 0

Euler’s identity is often cited as an example of deep mathematical beauty.

Constance Reid: Euler’s identity is “the most famous formula in all mathematics”.

Euler’s Identity is a special case of his formula from complex analysis suggested by Swiss mathematician Euler in  1748.

The identity links five fundamental mathematical constants:

  • The number 0
  • The number 1
  • The number π (π = 3.141 . . .)
  • The number e (e = 2.718 . . .)
  • The number i, the imaginary unit of the complex numbers.

Euler’s Identity “is absolutely paradoxical; we cannot understand it, and we don’t know what it means, but we have proved it, and therefore we know it must be the truth”. – Benjamin Peirce.

aplusclickEulerIdentity

The Largest Known Prime Number

The largest known prime number was discovered in 2016 by a computer laboratory of the University of Central Missouri .

257,885,161 – 1

is one of the Mersenne primes that can be written in form 2n – 1, where n is an integer.  They are named after 17-century French mathematician Marin Mersenne.

nums

The number written in the decimal form contains 17 million digits.

Why Is X The Unknown?

Terry Moore explains that the inventors of algebra were Arabic scientists. Their definition:

X = something, some undefined unknown thing = the unknown thing.

When the books were translated from Arabic to Spanish the Arabic unknown was “SH” that did not exist inSpanish. They replaced it by “X“.  It migrated to other European languages 600 years ago.

X is “X” because Spanish language does not have “SH“.