There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
by Nikolai Lobatchevsky

For Mirella

I’m compiling here the list of lectures that I have given or intend to give for my daughter Mirella. The oral lectures are given in French, but the texts written afterwards are in Vietnamese. I’ll make them into a book for school children.

(1) A Steiner problem: shortest path connecting the 4 vertices of a square. [optimization / variational methods]

(2) Polygons and their symmetry groups [group theory]

(3) Square wheels! [geometry, engineering]

(4) Princess Dido’s problem [optimization / variational methods]

(5) Walking ants problem [mathematical reasoning]

(6) Turing a square into an equilateral triangle [geometry, logic]

(7) Fibonacci numbers and exponential series [algebra, analysis]

(8) Cows eating grass problem [linear algebra]

(9) Gorilla selling bananas [optimization]

(10) Tessellations [geometry, transformation groupoids]

(11) Calculating 1^2 + 2^2 + … + n^2 [algebra, recurrence]

(12) What is integral [calculus]

(13) Which way takes less time?  [classical mechanics / variational methods]

To come:

* Strategies in war games [convex optimization]

* Bernoulli’s brachistochone [optimization / variational methods]

* What is derivation [calculus]

* Orbits [mechanics / analytical geometry]

* Curves of infinite length [fractal geometry]

* Crazy loto [diverging series]

* Snowflakes [symmetry in nature/ combinatorics]

* Chocolate eating game [combinatorics / logic]

* Seven Bridges of Königsberg (lementary topology / graph theory)

* Mobius band (simple topology)

* Eratosthenes measuring the earth (geometry)

* Pinnochio’s nose (logic)

* Optimal polygons

etc.

 

 

 

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