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There are a lot of curious things about the number 153. Just for starters:
It's a triangular number. 1+2+3+4+...+16+17 = 153.
It's the sum of the first five factorials: 1!+2!+3!+4!+5! = 153.
It's the smallest three-digit number that can be expressed as the sum of cubes of its digits. 1³+5³+3³ = 153.
And moving from mathematics to history, there are multiple connections between 153 and...fish. Yes, fish. The number 153 appears in the Gospel of John: after his resurrection, Jesus appears to his disciples, and having fished all night with no results, they then miraculously catch 153 fish. Why is the number of fish even mentioned?
There is perhaps a clue in a tale told by Iamblichus, in which Pythagoras, while journeying from Sybaris to Crotona, is said to have met some fishermen, who were drawing their net heavily laden to the shore, and he told them the exact number of fish they caught. In this story, the exact number is not mentioned. But Pythagoras was of course a mathematician, and the number 153 held some fascination for mathematicians at the time, because of a geometric figure known as the Vesica Piscis or "bladder of the fish".
The figure is simple: it's two intersecting circles, drawn in such a way that each one passes through the centre of the other. The lens-like shape formed by their intersection was thought to look like a fish's bladder, and if it is augmented by short segments of the circles just above them, looks very much like the Christian fish symbol - which is known to be ancient, but whose origins are obscure.
It's fairly easy to show* that the ratio of the height of the bladder to its width is √3. And the quantity 265/153 is very close (to within one part in 50,000) to √3. So was the mention of 153 in the gospel story an oblique reference to Pythagoras via the fish symbol? We will probably never know.
There is a modern twist, though. We are carbon-based life forms, and if you multiply 153 by the atomic weight of carbon (12), you get 1836, which is almost exactly the value of a fundamental constant of physics: the ratio of the mass of the proton to the mass of the electron. Coincidence? You decide.
*This is a phrase that maths tutors use when they are pretty sure something is true, but they have a feeling it is going to involve a lot of tedious algebra to prove it, and are worried about making embarrassing mistakes if attempt to do so in front of a student.
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