In 2011, Monash University mathematician Burkard Polster set out to answer a practical question: How precariously can you place a laptop computer on a crowded bedside table so that it will take up minimal space without falling off?
Assuming that both the table and the laptop are rectangular, and that the laptop’s center of gravity is its midpoint, it turns out that the optimal placement occurs when the laptop’s midpoint coincides with one of the table’s corners and the footprint is an isosceles right triangle, as above.
This also assumes that the table is reasonably sized. But then, if it’s tiny, then balancing a laptop on it probably isn’t your biggest problem.
(Burkard Polster, “Mathematical Laptops and Bedside Tables,” Mathematical Intelligencer 33:2 [July 2011], 33-35.)