Dzień Odkrywców Kampusu Ochota

 In this lecture, we'll dive into the fascinating world of some  recurrence relations--simple equations that generate complex  patterns--and uncover their surprising connections.

 We will start by revisiting familiar concepts like the geometric  series, the Fibonacci sequence, and Pascal's triangle, showing how  they build upon themselves to create intricate structures.

 Now, take a moment to imagine: when two particles collide elastically,  their total momentum and energy remain the same before and after the  collision. This is a fundamental rule of nature. But here's where  things get fascinating: if you measure the velocities of three  particles after each one collides elastically with the others, you'll  discover something surprising.  Whether the 1st particle collides with the 2nd, then with the 3rd, and  finally the 2nd interacts with the 3rd, or if you reverse this order,  the final velocities remain the same!

 But what do these elastic collisions of point-mass particles have to  do with the sequences of numbers we mentioned earlier, like the  Fibonacci sequence? In this lecture, we'll answer this intriguing  question and reveal how these seemingly unrelated ideas come together  in unexpected and elegant ways.

Preferred age of participants - last two years of secondary school.