Web Paint-by-Number Forum
Comments on Puzzle #30283: A Beautiful Identity
By sanane samanye (maceraseven)

peek at solution       solve puzzle
  version: 2    quality:   difficulty:   solvability: line logic only  

Puzzle Description:

Euler's identity is often cited as an example of deep mathematical beauty. Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation.

#1: Bruce Yanoshek (yanogator) on Oct 3, 2017 [SPOILER]

It's a very pretty puzzle, but it has a few problems, mathematical and otherwise:
1. e^pi*i = -1, not 1. Euler's identity is usually expressed as e^pi*i + 1 = 0, so when you take the 1 to the other side, it has to become negative.
2. Your statement of the identity doesn't have the addition in it, which makes your "Puzzle Description" sound a little strange.

The important thing, though, is that I enjoyed solving it. That's why it's here.
#2: Web Paint-By-Number Robot (webpbn) on Oct 3, 2017
New version published by maceraseven.
#3: sanane samanye (maceraseven) on Oct 3, 2017
Thank you for the warning. I am terribly ashamed to about the minus sign, and I corrected it. However, I will not change the equation further. There is no need for a plus sign when there is a equals sing.
#4: robert svanberg (tango) on Oct 3, 2017
Thank you. As a non-mathematician I knew about all the constants and operators here but had no idea that there was an identity linking them so elegantly. Thank you for enlightening me, plus the pretty solution.
#5: Aurelian Ginkgo (AurelianGinkgo) on Oct 3, 2017
Response to #4: Wait, solution? We're getting into chemistry now? (lol, just playing with words)
#6: Norma Dee (norm0908) on Oct 3, 2017
Over my head. :)
#7: Gator (gator) on Oct 3, 2017 [SPOILER]
How many mathematicians does it take to change a light bulb?

-e^i*pi

:)
#8: Kristen Vognild (kristen) on Oct 4, 2017
nice. :)
#9: David Bouldin (dbouldin) on Oct 4, 2017 [SPOILER]
Watched a pretty cool video recently that was looking at i^i...which relates to this:

https://www.youtube.com/watch?v=9tlHQOKMHGA
#10: Garden Pretty (DotyRoberts) on Oct 6, 2017
I've enjoyed the logic of your logic puzzles.
#11: Bruce Yanoshek (yanogator) on Sep 15, 2022 [SPOILER]
Sanane,
Your correction is good, but in your description, you say that it contains an addition. That is the problem I was alluding to. The way the - sign grows out of the black background is nice.
#12: Bill Eisenmann (Bullet) on Sep 15, 2022
I can't tell you how much I miss Sanane's puzzles :(((

Goto next topic

You must register and log in to be able to participate in this discussion.