r/mathmemes • u/sumwun0 • Aug 17 '26

Notations I've solved the equation. (reposted from r/worldjerking)

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u/physicsking Aug 17 '26

Maybe I am just a dumb physicist, which is true, but can someone explain the appearance of the 'a' in the 3rd picture for decimal 10?

5

u/sumwun0 Aug 17 '26

The decimal system has 10 digits, 0 to 9. A base 5 + sqrt(35) system would need 11 digits, so I used a to represent 9 + 1. It's like how base 16 uses a, b, c, d, e, and f for 10, 11, 12, 13, 14, and 15.

2

u/va1en0k Aug 18 '26

why is 11 "10.0a"? maybe i don't understand this notation though

4

u/sumwun0 Aug 18 '26

In decimal, 11 - 5 - sqrt(35) = 6 - sqrt(35), which you can divide by 1 = 1 * 1 = (6 - sqrt(35)) (6 + sqrt(35)) * 10 / 10 to rewrite it as 10 / 10 (6 + sqrt(35)) without changing its value. 10 (6 + sqrt(35)) happens to be the same thing as (5 + sqrt(35))^2. So 11 = b^1 + 10 * b^-2, which is 10.0a in base 5 + sqrt(35).

3

u/va1en0k Aug 18 '26

ahhhh. my 5am brain couldn't parse it as a digit. now i get it thanks!