# M3.3.12

**ratios**.

### Why is Summer Hot?

It is quite common for people to believe that summer is warmer than winter,

basing the explanation on the belief that Earth is closer to the Sun during the

summer than in the winter. Even a sizable fraction of Harvard graduates carry

this belief (Schneps, 1987, mentioned in Green, 2003). In reality, this is exactly

opposite the situation in the northern hemisphere. The separation of Earth and

Sun is greatest at the beginning of July and least at the beginning of January.

More direct sunlight and the greater duration of daytime in summer months

### Square Root of 2: Irrational, Yes! Impractical, No!

For the mathematically inclined person, irrational numbers such as a^{2} are fascinating, both from a historical perspective, and as a classic example of using the reductio ad absurdum proof, to prove the irrationality of a^{2}. However, the majority of students, when introduced to the irrational number a^{2}, might be excused for not being fascinated by it, and might believe that a^{2} has not much practical use.