1.
In one of his books, Isaac Asimov described the communication between a human and an alien. Imagine that you are in the place of this person and you know the following principles of the aliens’ mathematics:

You want to explain to him explain how gravity acceleration works on your planet by describing the

following formula in their Math language:

S = vt + 4.9t2

How will this formula look in the mathematical language of the alien?Deselect Answer

2.
The most efficient way to pack many spheres into a given volume is to use a regular, hexagonal lattice. This fact has been ‘known’ to us for thousands of years, yet it was only mathematically proven in 1998 by Thomas Hales. It has many profound implications on our daily lives, from stacks of groceries and cannonballs, to the atoms in a crystal.

Let us consider the simpler 2D case. Those who play pool, will know that the most efficient way

to “squeeze” circles into a given area is to use hexagonal packing, as shown below

Packing efficiency is defined as how efficiently the space is used, i.e. the area of the circles divided

by the total area used (including ‘between’ circles). If the 2D hexagonal packing is extended

infinitely, what is the packing efficiency?Deselect Answer