Cooking Maths

Whether you believe it or not, Maths are everywhere around us, even on our plate!

Easter cookies and the Gordian knot




Happy Easter from the Pomegranate team!

The Gordian knot, was an intricate knot used by Gordius to secure his oxcart.

An oracle informed the people that their king would arrive in a wagon. When Gordius arrived in Phrygia’s central square in his oxcart, people declared him their king.

That’s why Gordius dedicated his oxcart to Zeus and tied it up with a peculiar knot…The Gordian knot. It had no beginning and no end!

Another prophecy stated that he who would untie the knot would become the ruler of Asia.

Many people tried to undo the knot but with no success, until Alexander the Great, with a stroke of his sword, managed the impossible!

The Pomegranate team makes their Easter "Gordian" cookies!

Maths and chocolate

Solving a problem becomes easier when someone has been drinking a big amount of chocolate. That’s because chocolate consists of flavonols, which belong to the flavonoids. Flevonoids are antioxidant substances that are good for the human brain.

Moreover, the consumption of chocolate helps someone to not get tired, mainly mentally. That’s what a new scientific research from Britain found out. They came to the conclusion that chocolate is beneficial for those that often get involved into mentally trying activities. Flavonols are part of the chemical substances, called polyphenols that increase the blood flow through the brain. Finally, the researchers said that we should consume flevonols on a regular basis ‘cause they also exist in fruits and vegetables’.

Summarized from the Greek local press by Foteini

To understand this equation, visit our posts for Valentine's day!

Eating Fermat's last theorem!

A 350 years old enigma on the margin of a book

Pierre de Fermat was a 17^th century lawyer and at the same time one of the world’s most important mathematicians. His contributions encompass a wide range of domains, from number theory, calculus, algebra, analytic geometry and optics. A few important theorems and conjectures bare his name, some of which have been a challenge to mathematicians for centuries.

One of these is known as Fermat’s Last Theorem, actually a famous conjecture he first wrote in 1637 on the margin of a page of Arithmetica. He claimed having a complete proof, but being unable to reproduce it on such a small place. No successful proof was published until 1995 despite the efforts of many mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th. It is among the most famous theorems in the history of mathematics and prior to its 1995 proof was in the Guinness Book of World Records for "most difficult math problem".

The theorem states that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than two. (For n=2 there are an infinite number of such triplets, namely the Pythagorean numbers, such as 3, 4, 5 or 5, 12, 13). Proofs have been found for particular numbers, but the general correct proof has only been given by Andrew Wiles in 1995. Thus, Wiles was the winner of the competition that had been launched one hundred years before and he collected the 50000$ prize.

According to mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."

Bucarest sent us the text and Elefsina made the theorem out of waffers, did some research on the Internet, marvelled at the story. It was the suitable thing to do for a problem that has eaten up so many mathematicians! As you can see, our students developped quite an appetite for math books in the library!

And here is Google's Doodle on Fermat: (“I have discovered a truly marvelous proof of this theorem, which this doodle is too small to contain.”)

A Challenge: Make a fractal salad!

Fractals are one of the most famous terms in modern Mathematics. Basically, a fractal is a geometric shape that can be split into parts each of which is similar to the whole. The process can go on infinitely. This property is called self-similarity. Fractals are easily found in nature: think of a snow-flake, a cauliflower or a fern leave! But their applications are quite diverse, from science to art and music. You can find out more about them here or here.
And now, our first challenge: make a fractal salad, take a picture and upload it here!
You can find inspiration and hints about the fractals in the kitchen on this page! 
Enjoy the challenge and the salad!
See how you can turn a triangle, a snowflake or a carpet into a fractal!
And here is a fractal tree: Pythagora's tree.

 

 

Can you find  the root of the next equation?

2(x+shake) + shake/2 = milkshake + 3shake/2 + x

Hint: white, liquid, cats like it…

Solution:

 2x + 2shake + shake/2 = milkshake + 3shake/2 + x

2x – x = milkshake + 3shake/2  - 2shake – shake/2

x = milkshake – shake

x = milk


A taste of infinity

This is a chip eaten on our first chat day, November 17th. Doesn't it look like the infinity symbol  ∞ ? Let's find more edible math symbols!

 

 

 

Double root

 A function or an equation has double roots (double solutions) when two of its roots/solutions are equal. This can happen for example for a quadratic function/equation.

A quadratic equation will have two solutions and thus two roots. There will be a double root if the two roots are equal. This occurs when the quadratic is a perfect square trinomial: x ² ±2 ax + a ² ; that is, when it is the square of a binomial: ( x ± a )². For example, for  f ( x ) = x² −10 x + 25, x=5 is a double root; or  for (x-1)²=0, x=1 is a double root.

However, this carrot can explain better what a double root is!

Square Root and Cube Root

Photo Cube

Funny Food formulas

Maths and cooking are much more similar than we think. Any dish relies on an precise formula, while a cookbok is nothing but a collection of algoriths, of step-by-step instructions and processes. Just  as well, we could say we have a “recipe” for multiplying numbers or for solving equations.

Here are some funny “formulas”: for making bread, a hamburger and even one for a book.

So, you can tell your mother: “While I am cooking my Maths homework, can you compute a chocolate cake for me, please?”

Biscuits recipe from the Avila team
The Spanish team sent this yummy recipe, take care of the proportions!

Biscuits from Avila

Well, we tried the Avila cookies at school and a Pomegraneate mom made them at home.

And you know what? ATOM is in its second month, and it has already altered the way we see things around us. Take a look at Elefsina ancient ruins. Now isn't that an Avila cookie?

Actually, the Avila cookie is a reflected Archimedean spiral like this one.
More about this kind of spiral and some other ones here.

Hyperbola

In Greek hyperbole means exaggeration. Take a look at what happens if we overdo it in AToM kitchen!

Find out more about hyperbola.