M3.3.12

Solves real-world problems involving 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

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

For the mathematically inclined person, irrational numbers such as a² are fascinating, both from a historical perspective, and as a classic example of using the reductio ad absurdum proof, to prove the irrationality of a². However, the majority of students, when introduced to the irrational number a², might be excused for not being fascinated by it, and might believe that a² has not much practical use.

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