## Space filling curve

Posted on: November 29th, 2014 by
1

Can you find a continuous function from the unit interval $[0,1]$ to the unit square $[0,1]^2$? In other words, can you find a curve that passes through all points in a unit square?

## Coin covering puzzle

Posted on: November 27th, 2014 by
2

100 identical circular coins are placed in a rectangular table such that no extra coin can be placed without overlapping with one of the coins already on the table. For the purpose of this puzzle, assume a coin is placed on a table as long as it's center lies on the table. Show that with 400 coins, one can cover the entire surface area of Continue reading the story "Coin covering puzzle"

## Parabola puzzle

Posted on: November 25th, 2014 by
Let $y=ax^2+b_1x+c_1$ and $y=ax^2+b_2x+c_2$ be two parabolas with the same coefficient for the $x^2$ term. The y-intercepts of the two parabolas are $(0,c_1)$ and $(0,c_2)$ respectively. Let the two parabolas intersect at $(x_1,y_1)$ and let the tangent to the two parabolas drawn at $(0,c_1)$ and $(0,c_2)$ intersect at $(x_2,y_2)$. Show using physics that $x_1=x_2$. Hint: Assume x is time and y is space, and there is Continue reading the story "Parabola puzzle"