There are deep and beautiful relationships between a function, its first derivative, its second derivative and its successive derivatives. A *k* derivative *y-value* reflect the *rate of change* of the *k-1* derivative.

Here’s a demonstration trying to show that *magic interplay* between a function, its first derivative and its second derivative.

# Monthly Archives: February 2014

# The early universe as seen by the ESA’s Planck space telescope

More info… (link to the ESA’s *Planck project* website)

# The “dice roll with a given sum” problem

In some exercise taken from combinatorics textbooks you might find a question like: “*if you roll 2 dice what is the probability to get 9 for the sum of the 2 dice faces?*”

The answer is not much difficult and can be intuitively given by enumerating the number of cases that satisfy the given event and dividing that number with the number of all possible outcomes.

But what if you want to find the probability of, say, a sum of 31 when rolling 10 dice, where simple enumeration would require a very long time? Or to find a more general formula for the probability of getting *p* points as the sum of rolling *n* dice? Is there such a formula, computable without having to enumerate all the cases?

# A nice (but not easy) combinatorics problem

Eight celebrities meet at a party. It so happens that each celebrity shakes hands with exactly two others. A fan makes a list of all unordered pairs of celebrities who shook hands with each other. If order does not matter, how many different lists are possible?

*Annual Harvard-MIT Mathematics Tournament 2006*