Take a photo of a barcode or cover
brettt 's review for:
People who think that ridding humanity of religion and such will remove the weirdness and episodes of random oddball wackiness from the world will probably continue to be disappointed as long as there's math around. Case in point is an irrational number that goes by the name phi or the Greek letter Φ. Like its more famous cousin π, Φ comes from a geometric relationship. It's a way to divide a line in such a way that the ratio of the two unequal pieces added together to the longer piece is the same as the larger piece to the smaller one. And like the other one, it never repeats and never ends, starting out as 1.618033 and going on from there.
The ancient Greeks calculated the number which is called the Golden Ratio because of it's aesthetically pleasing quality. But things started to get weird when Φ started showing up in nature. Such as the spiral shell of a nautilus, which spiraled inward along the same ratio as the line. Botanists found it showing up in the distribution of leaves on a tree branch -- if not exactly, close enough often enough to be significant. Modern researchers have found it in different qualities on the molecular level.
Astrophysicist Mario Livio, in 2003's The Golden Ratio, reviews some of the places Φ is supposed to have shown up across history. He finds that in a lot of those cases, Φ's either not really there or the similarity to it is something of a coincidence. It probably didn't influence the construction of the pyramids or the way Da Vinci painted Mona Lisa, for example. But it does show up in enough different places to be weird enough.
The chapters get a little repetitive and it's possible that Livio could have dropped one or two suspected appearances of the Ratio that turned out to be incorrect. But he's a gifted science writer with a real knack for moving complicated concepts into the realm of lay understanding, and he leaves plenty of room for a readers to figure out for themselves what they think about the prevalence of Φ in the universe and why this particular mathematical expression shows up as often as it does in the real world.
Original available here.
The ancient Greeks calculated the number which is called the Golden Ratio because of it's aesthetically pleasing quality. But things started to get weird when Φ started showing up in nature. Such as the spiral shell of a nautilus, which spiraled inward along the same ratio as the line. Botanists found it showing up in the distribution of leaves on a tree branch -- if not exactly, close enough often enough to be significant. Modern researchers have found it in different qualities on the molecular level.
Astrophysicist Mario Livio, in 2003's The Golden Ratio, reviews some of the places Φ is supposed to have shown up across history. He finds that in a lot of those cases, Φ's either not really there or the similarity to it is something of a coincidence. It probably didn't influence the construction of the pyramids or the way Da Vinci painted Mona Lisa, for example. But it does show up in enough different places to be weird enough.
The chapters get a little repetitive and it's possible that Livio could have dropped one or two suspected appearances of the Ratio that turned out to be incorrect. But he's a gifted science writer with a real knack for moving complicated concepts into the realm of lay understanding, and he leaves plenty of room for a readers to figure out for themselves what they think about the prevalence of Φ in the universe and why this particular mathematical expression shows up as often as it does in the real world.
Original available here.