Some, like Kepler's Laws, changed our science. Others are simply startling. Pythagoras was so spellbound when he realized that the square of any right triangle's sides add up to the square of its hypotenuse, he supposedly sacrificed 100 oxen to honor the gods. Such a stunning relationship between Nature and numbers had to be divine, he reasoned. Fortunately for him, the animal rights office was closed that day.
Maybe you don't love math. But I have to tell you, there are some freakish links between numbers and planets. Most famous is the strange sequence published in the 18th century. Take the pattern 0, 3, 6, 12, 24, 48, 96 - which keeps doubling. Add four to each, insert a decimal point, and weirdly enough you get a sequence that accurately expresses each planet's distance from the Sun. Here's the progression - which was soon called Bode's Law - along with the actual planet distances in Earth-Sun units, or AUs: Mercury 0.4 (actual is 0.39), Venus 0.7 (actual 0.72), Earth 1.0 (1.0), Mars 1.6 (1.52), empty 2.8, Jupiter 5.2 (5.2) and Saturn 10.0 (9.54).
When Bode popularized this in 1768, nothing matched the 2.8 and no planet lay beyond Saturn's 10. But William Herschel soon found Uranus, and wham! It nicely fit the next Bode number, 19.6 (actual distance: 19.19). Then came Ceres in 1801. First considered a planet (and now once again promoted to "dwarf planet" status), it nailed that empty 2.8 gap to perfection. The whole thing worked.
Trouble was, no physics can explain this neat way in which the planets are ordered. It's math without science. When Neptune was found in 1846 and didn't match, the pattern was quietly dismissed as just a wild coincidence.
But is it? These days some astronomers think orbital resonances - the way planets interfere with others - may be responsible, so Bode's Law may be valid after all.
The sky is riddled with math oddities. The Moon is 400 times smaller than the Sun, but also 400 times closer, making them appear the same size. And both spin at virtually the same rate of 27 days. Just amazing coincidences, right?
There are other bewildering patterns, too - like the bizarre giant hexagon found at Saturn's North Pole, which researchers are just beginning to get a handle on. These days we seem teased by elegantly simple math in odd places.
It's good that Pythagoras is no longer with us. No animal would be safe.