A lot of our archived debates centered around how we might redesign (reform) the curriculum in light of computer languages, Python in particular.
What I'm coming to lately is emphasizing arbitrary precision e.g. pi to literally a thousand places, as an especially attractive feature of computers in general. Mere calculators don't usually do arbitrary precision (I remember one Casio (?) with a scrolled display), but seem more reliable in giving the expected grade school results vs. answers we might get from using floating points (IEEE 754), which bring their own form of disillusionment. In other words, in going from a basic math topic, such as irrational numbers, to computers, why not emphasize the extrapolation of our algorithms to large numbers of decimal digits? Lets compute Phi as (1 + sqrt(5))/2 to hundreds of digits and check published sources (such multi-digit comparisons might mean converting to strings). We've done stuff like that around pi here on edu-sig, computing from algorithms (one of Ramanujan's in particular). These arbitrary precision numbers may not have much use in scientific and engineering applications (because nothing gets measured to that degree of precision) but I'm talking about bridging from math, so-called "pure math" in particular. My approach of late has been to use geometric objects (volumes, polyhedrons) and check that our computations may be exact to several hundred decimal points thanks to Python's Decimal. I also use the 3rd party gmpy2 library. Here's an essay on Medium if you'd like to read more: https://medium.com/@kirbyurner/calculator-of-tomorrow-using-arbitrary-precision-8f219b0092d9 Kirby
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