Moontower Munchies #134
I love this Vonnegut quote!
I came to the same math understanding too late when I struggled with linear algebra. If I had just "accepted" it earlier (rather than try to "intuit" it) I may have actually become an engineer 😂
Just to help out a bit (😅, 😅)
2^(1/2), 2^(1/3), 2^(1/4), 2^(1/5), 2^(1/6), …, 2^(0).
Here are values (rounded):
2^(1/2) = √2 ≈ 1.41421356
2^(1/3) ≈ 1.25992105
2^(1/4) = 2^(0.25) ≈ 1.18920712
2^(1/5) ≈ 1.14869835
2^(1/6) ≈ 1.12246205
… =>(values decrease toward 1 as denominator increases & power decreases to 0) =>2^0 = 1
■ Intuitively as "radial stretching". Geometric (unit‑circle) analogy:
Euler’s formula e^{iθ}=cosθ+i sinθ maps rotations on the unit circle.
e^{t} (real t) is a radial stretching by factor e^{t}; 2^(1/n)=e^{t} is a small radial stretch when t=(ln2)/n is small.
So as n increases, the stretch approaches 1 (no radial change), analogous to shrinking a rotation/stretch toward the identity on the complex plane.
You're making me want to take math again! Don't really understand it but it looks fun
I love this Vonnegut quote!
I came to the same math understanding too late when I struggled with linear algebra. If I had just "accepted" it earlier (rather than try to "intuit" it) I may have actually become an engineer 😂
Just to help out a bit (😅, 😅)
2^(1/2), 2^(1/3), 2^(1/4), 2^(1/5), 2^(1/6), …, 2^(0).
Here are values (rounded):
2^(1/2) = √2 ≈ 1.41421356
2^(1/3) ≈ 1.25992105
2^(1/4) = 2^(0.25) ≈ 1.18920712
2^(1/5) ≈ 1.14869835
2^(1/6) ≈ 1.12246205
… =>(values decrease toward 1 as denominator increases & power decreases to 0) =>2^0 = 1
■ Intuitively as "radial stretching". Geometric (unit‑circle) analogy:
Euler’s formula e^{iθ}=cosθ+i sinθ maps rotations on the unit circle.
e^{t} (real t) is a radial stretching by factor e^{t}; 2^(1/n)=e^{t} is a small radial stretch when t=(ln2)/n is small.
So as n increases, the stretch approaches 1 (no radial change), analogous to shrinking a rotation/stretch toward the identity on the complex plane.
You're making me want to take math again! Don't really understand it but it looks fun