You’re right, it’s odd that the article mentions memorization. That’s not what makes this interesting. Obviously bits is the relevant concept here from a moder

You’re right, it’s odd that the article mentions memorization. That’s not what makes this interesting. Obviously bits is the relevant concept here from a modern information theory perspective. But “digits in fraction” is more interesting. 22/7 vs 314/100. 355/113 vs 3141592/1000000. Of course you don’t need to “remember” the denominator when it is a power of 10. But the error in the approximation is unusually low, compared to the size of the denominator. This is true when comparing to decimal approximations, or other “nearby” rational approximations. In that sense, these approximations should be “surprising” because they work much better than the decimal ones of similar size (or, much smaller than the decimal approximations of similar accuracy). But they also work better for pi than for many other common irrational numbers. This is also historically meaningful, as some calculation was done in fractions, e.g. in ancient Egypt. It is an interesting mathematical fact that 22/7 is an approximation to pi that is small enough to be easily discoverable, easy to compute with, and still practically useful.