boyobo

9 ms·

31.
by boyobo 7y ago
The factors of 27 are 1,3,9 and 27. That’s four factors. That's why door 27 is closed at the end of the open/closing process - employees 1,3,9 and 27 touch the door and so the final state of the door is the same as the initial s
32.
by boyobo 7y ago
Simpler explanation for why perfect square <=> odd number of factors Proof: For every divisor d of n, n/d is another, different, divisor. This gives a pairing of all the divisors. The only exception is if n/d = d. The except
33.
by boyobo 7y ago
I am giving an alternate proof of your implicit statement "There exists a line which has the same number of points on each side". You did this by computing duals of cell arrangements. I am arguing that you don't need to do th
34.
by boyobo 7y ago
> Check out William Bricken's "Iconic Math" http://iconicmath.com/ or "Proofs without Words" https://en.wikipedia.org/wiki/Proof_without_words or the other 3Blue1Brown video
35.
by boyobo 7y ago
Are you trying to say that math is hard because the teachers are withholding all the tricks? > I am questioning their utility as an educational device. Puzzles like this aren't found in mainstream math education contexts. As you ack
36.
by boyobo 7y ago
Just pick a point and rotate a line around that point continuously. Keep track of the number of points on the left. Since this count is essentially continuous (the jumps are of size 1), at some point during this rotation you will have an
37.
by boyobo 7y ago
> > say $150,000 to not teach 2 classes for a year Is that why she is teaching two classes in her first semester, including one which is lower division? Not really sure what you're saying. The fact that she's teaching just m
38.
by boyobo 7y ago
Uh-oh, I think I might be doing this (as a college lecturer). Do you have some references, or some examples of how this might arise in a classroom?
39.
by boyobo 7y ago
If we just throw our hands up in the air and declare everything a "miracle" we never learn anything.
40.
by boyobo 7y ago
I would say it's not as interesting because a high-schooler (or Pythagoras) could easily verify the fact AND they would easily be able to explain how you came up with that sum. One of my metrics for determining if a fact F is interest
41.
by boyobo 7y ago
I'm not sure exactly what you mean here but there I can't think of an interpretation that makes your statement close to being true. e.g. 1+4-9+16-25+36-49=-26
42.
by boyobo 7y ago
i= sqrt(-1) https://en.wikipedia.org/wiki/Euler%27s_identity
43.
by boyobo 7y ago
Ah, I didn't realize that's what you were trying to say with the explanation at the beginning. Now your post makes more sense.
44.
by boyobo 7y ago
Let's just let each other be excited about our favorite math, okay? I don't think it's malicious, we're just trying to narrow down exactly what makes something interesting. In the process, we get to understand ou
45.
by boyobo 7y ago
Fair enough. I do see how you could think that it's intuitive. I've even used your explanation when I'm teaching. Although I can't help but think there's some sort of circularity going on here, at least for me. My i
46.
by boyobo 7y ago
Everything you said seems to be valid if you replace 'exponential' by 'f' where 'f' is any real analytic function.
47.
by boyobo 7y ago
Your explanation is a nice restatement or interpretation for what the equation f(x)=f(0)+f'(0)x+.... is saying, but it doesn't give any insight for why the equation is true. and as there is no additional change that comes
48.
by boyobo 7y ago
Analytic functions are usually defined to be those functions which can be represented by their Taylor series. This is what I meant by `tautological'.
49.
by boyobo 7y ago
Let's take "analytic" to mean "determined by its maclaurin series". It's not surprising that polynomials are analytic. Look at the definition of a polynomial. It's already in "power series" form,
50.
by boyobo 7y ago
Write down the first 50 terms of the series for e^{-x}. Go back in time and tell Pythagoras to plug in x=2,3,4,5,6,7,8,10,... Each of the terms is a rational number, and the each of the sums will be an extremely small rational number (nume
51.
by boyobo 7y ago
This seems pretty tautological to me. this is not true of all functions... But it is true for very large classes of functions Which classes of functions? It sounds like you're saying that a function is determined by its derivat
52.
by boyobo 7y ago
I am a novice programmer who started with python and have recently been using javascript, where I use auto-indent-on-save. Coming back to python is annoying because it's harder to make sure code is at the right indent level than to use
53.
by boyobo 7y ago
Ironically for me, the humanities people that it was aimed at often took it amiss. Dan Dennett told me as much. throwawayjava thank you for the suggestion; I'll use it in a footnote in the next iteration! Yes, I thought this article
54.
by boyobo 7y ago
It's an introduction to the fundamental concepts of information theory (entropy, KL divergence, conditional entropy), using 20 questions as an ongoing source of example applications and interpretations of these concepts. The author als
55.
by boyobo 7y ago
The problem is that we haven’t defined what we’re measuring. E.g. Usain bolt makes far more than 10x money from running than the average healthy adult.
56.
by boyobo 7y ago
I don't see how this solves the problem. What happens when your 'link aggregator'? decides to ban certain content?
57.
by boyobo 7y ago
How about this: People shoot in a random order (now everyone has the same chance of making it to the next round. Is it 1/e?) import numpy as np class Shooter: def __init__(self): self.dead = False self
58.
by boyobo 8y ago
In an idealized economic model, "rich developers" will get their desired domain names anyway as they can offer a large sum of money to the "poor developers" to give up their domain name. https://en.wikipedia.o