Search found 3095 matches

by Qaanol
Sun Apr 21, 2019 12:18 pm UTC
Forum: Mathematics
Topic: Show that a triangle is right angled
Replies: 2
Views: 883

Re: Show that a triangle is right angled

Height of what, bisector of what, and median of what?

Try drawing a picture.

Is this homework?
by Qaanol
Mon Apr 01, 2019 4:48 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 2131: “Emojidome”
Replies: 123
Views: 14618

2131: “Emojidome”

https://imgs.xkcd.com/comics/emojidome.png https://xkcd.com/2131/ Alt-text: “&#129340&#129340&#129340&#129340&#129340&#129340&#129340&#129340” (I tried to paste in the actual emoji, but when I go to post the forum won’t let me, giving the error message “Your message ...
by Qaanol
Thu Feb 28, 2019 4:04 am UTC
Forum: Individual XKCD Comic Threads
Topic: 2117: "Differentiation and Integration"
Replies: 45
Views: 7534

Re: 2117: "Differentiation and Integration"

And I still feel a little guilty that I never got around to figuring out complex analysis. I recall in "Surely You're Joking, Mr. Feynman", he suggests doing away with it and using differentiation under the integral sign instead, which I never figured out either. Oh well. The nitty-gritty...
by Qaanol
Sat Feb 09, 2019 8:38 pm UTC
Forum: Mathematics
Topic: The frog riddle
Replies: 23
Views: 4788

Re: The frog riddle

As a probability puzzle, it is pretty straightforward and the narrator does a decent job of explaining it. Qaanol, the narrator says that each frog's sex is independent. No, the narrator’s statement of the puzzle does not say that. It does say that male and female frogs occur in equal numbers, but ...
by Qaanol
Tue Feb 05, 2019 1:19 am UTC
Forum: Mathematics
Topic: The frog riddle
Replies: 23
Views: 4788

Re: The frog riddle

There is not enough information provided to solve the puzzle. We would need a model for the social behavior of frogs, to determine the probability that a pair of frogs found together would have each possible combination of genders, as well as the probability that a lone frog would be male or female.
by Qaanol
Sat Jan 12, 2019 8:05 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 151883

Re: Math: Fleeting Thoughts

This is good pedantry, but Qaanol's wasn't. You can't just take any number and say it's a percentage by multiplying it by 100; percentages *mean* something, dang it! (In this case, the correct answer is "a degree is approximately 1.75% of a radian". The fact that a radian is just the unit...
by Qaanol
Thu Jan 10, 2019 9:48 pm UTC
Forum: Mathematics
Topic: Favorite Mathematical Equation
Replies: 87
Views: 18472

Re: Favorite Mathematical Equation

Yakk wrote:I take your 1/5 and raise you iⁱ≈1/sqrt(20+pi), to a frankly ridiculous number of decimal places.

Today I learned that 5 is a frankly ridiculous number. This comports well with our existing knowledge that infinity and 5 are effectively indistinguishable.
by Qaanol
Thu Nov 01, 2018 5:03 pm UTC
Forum: Mathematics
Topic: How to find confidence interval for vector-valued function?
Replies: 5
Views: 3145

Re: How to find confidence interval for vector-valued function?

Adding a certain amount (x) of a reagent to a chemical solution, then measuring the concentrations of several different reaction products (should be g(x), actual measured values have some error). I want to know if the correct amount (x0) of the reagent was added.
by Qaanol
Wed Oct 31, 2018 11:51 pm UTC
Forum: Mathematics
Topic: How to find confidence interval for vector-valued function?
Replies: 5
Views: 3145

How to find confidence interval for vector-valued function?

I have a function f: ℝ→ℝ n that takes one input and produces n outputs. It represents the result of a physical process, and is equal to a theoretical model g(x) plus a measurement error. For a given sample, I can measure the values of f(x), and I want to find out the value of x. In particular, there...
by Qaanol
Thu Aug 09, 2018 12:04 am UTC
Forum: Science
Topic: Syllabus for learning advanced mathematics and physics for a highschool student.
Replies: 5
Views: 3391

Re: Syllabus for learning advanced mathematics and physics for a highschool student.

For mathematics, you will definitely want a solid grasp of linear algebra and differential equations. A significant part of physics comes down to partial differential equations, which can get…difficult. On the more theoretical side, you may want to learn about topology and manifolds. And, in light o...
by Qaanol
Sat Jul 14, 2018 4:49 am UTC
Forum: Computer Science
Topic: Help me prove (or disprove) the following problem NP-hard
Replies: 7
Views: 6644

Re: Help me prove (or disprove) the following problem NP-hard

I believe this is a linear programming problem—very nearly a textbook example of one—and as such can be solved in polynomial time.
by Qaanol
Sun Jul 01, 2018 9:54 pm UTC
Forum: Language/Linguistics
Topic: Oxford comma query
Replies: 28
Views: 11077

Re: Oxford comma query

It’s worth noting that ambiguity is *also* possible when an Oxford comma is included: “He thanked his mother, Athena, and his training staff.” If the second comma were removed, the sentence would have only one meaning. …and then there are sentences which are ambiguous irregardful of whether a second...
by Qaanol
Mon May 07, 2018 6:19 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1990: "Driving Cars"
Replies: 86
Views: 13980

Re: 1990: "Driving Cars"

Why is there a ghost behind Cueball?
by Qaanol
Mon Apr 16, 2018 10:18 pm UTC
Forum: Mathematics
Topic: Projecting a Polytope
Replies: 5
Views: 4511

Re: Projecting a Polytope

Thanks for the suggestion! I'm not sure how to get around the fact that x and y are in vector spaces of different dimension, though. I know that invertible transformations do exist, but I couldn't even begin to figure out how to construct T(t) which is invertible for t>0, but approaches something l...
by Qaanol
Mon Apr 16, 2018 4:24 pm UTC
Forum: Mathematics
Topic: Projecting a Polytope
Replies: 5
Views: 4511

Re: Projecting a Polytope

Here’s something to try:

Form a continuous family of transformations T(t) such that T(0) = C, and T is invertible when t≠0. For example, I think T(t) = t·I + (1−t)·C should work. Find the general solution in terms of T when t≠0, then take the limit as t→0.
by Qaanol
Fri Apr 06, 2018 9:20 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1977: "Paperwork"
Replies: 7
Views: 3569

Re: 1977: "Paperwork"

SonofRojBlake wrote:Wait... so Cueball has been naked this whole time?

Mind. Blown.

Going back to reread all the previous comics with that in mind.....


All xkcd characters are naked except when specifically shown wearing clothes.
by Qaanol
Mon Apr 02, 2018 9:02 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1975: "Right Click"
Replies: 42
Views: 19670

Re: 1975: "Right Click"

I found a typo in the Who’s On First section. When it gets to the pitcher and Costello asks “You don’t want to tell me today?” it has Abbott respond “I’m tell you, man.”
by Qaanol
Mon Apr 02, 2018 8:13 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1975: "Right Click"
Replies: 42
Views: 19670

Re: 1975: "Right Click"

If you beat Advent.exe you get an option to save the image. I'm not sure of any way to link directly to the result, so I'm going to imgur this. The URL from which the image downloaded for me is https://xkcd.com/1975/v6xso1_right_click_save.png . Not sure if that is a temporary address or permanent ...
by Qaanol
Tue Mar 20, 2018 11:07 pm UTC
Forum: Mathematics
Topic: A probability question
Replies: 5
Views: 4933

Re: A probability question

83.1 ~ 83.33... = 5/6 Take it up to 4 and see what happens? Guessing what's going on from one data point is going to be pretty impossible. I’ll try that when I have time to update the code. I’m trying to find an analytical solution. With n IID normal variates, their position in ℝ n is spherically-s...
by Qaanol
Tue Mar 20, 2018 8:56 pm UTC
Forum: Mathematics
Topic: A probability question
Replies: 5
Views: 4933

Re: A probability question

I had a silly typo in my simulation code.

The *actual* results are consistently close to 83.1% for H = J, and 6.4% for H = L.
by Qaanol
Sun Mar 18, 2018 6:43 am UTC
Forum: Mathematics
Topic: A probability question
Replies: 5
Views: 4933

A probability question

Here’s the procedure: • We choose n numbers from a standard normal distribution, and sort them so x 1 ≤ x 2 ≤ ⋯ ≤ x n . • Then we find the midpoint of each consecutive pair, m i = (x i + x i+1 ) / 2. • These midpoints partition the real line into intervals, one of which, call it J, contains 0. • If ...
by Qaanol
Fri Mar 16, 2018 4:22 am UTC
Forum: Computer Science
Topic: Looking for an algorithm to test for abridgement
Replies: 3
Views: 4429

Looking for an algorithm to test for abridgement

Here’s the scenario: • You have a book, and some of the words are underlined. • I hand you another book. • You have to figure out if it is possible to start with your book, erase some of the non-underlined words, and end up with my book (or at least, the same words in the same order as my book). The...
by Qaanol
Fri Feb 02, 2018 4:07 pm UTC
Forum: Mathematics
Topic: Mathematics of p-hacking: random walks and significance
Replies: 9
Views: 7154

Re: Mathematics of p-hacking: random walks and significance

>-) wrote:I'm under the impression if lim n -> inf of f(n) = infinity, then it means for every w, there exists n such that f(n) > w.


Not quite: that limit means for every w, eventually f(x) will never drop below w again. In other words, there exists n such that f(x) > w for *every* x>n.
by Qaanol
Tue Jan 30, 2018 11:56 pm UTC
Forum: Mathematics
Topic: Mathematics of p-hacking: random walks and significance
Replies: 9
Views: 7154

Re: Mathematics of p-hacking: random walks and significance

>-) wrote:For every real number w, there is an integer n, such that there exists an integer k >= n such that S_k/sqrt(k) > w, with probability 1.

Not quite: limsup means it keeps happening out to infinity. In other words, for *every* integer n there is a k>n with f(k) > w.
by Qaanol
Mon Jan 15, 2018 9:13 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1942: “Memorable Quotes”
Replies: 37
Views: 9020

1942: “Memorable Quotes”

https://imgs.xkcd.com/comics/memorable_quotes.png Mouseover: “"Since there's no ending quote mark, everything after this is part of my quote. —Randall Munroe” • • • Most xkcd comics have all text majuscule, but there is a lowercase letter in this one! Also, I’m probably going to use a few of t...
by Qaanol
Fri Dec 15, 2017 5:47 am UTC
Forum: Mathematics
Topic: Bump Function
Replies: 7
Views: 4739

Re: Bump Function

Okay, try this on for size: Can you prove that, for every positive integer n there exists a positive real number a n such that, if x is within distance a n of 0 then your function’s magnitude is less than the magnitude of x n ? In other words, by choosing x “close enough” to zero, can you show that ...
by Qaanol
Wed Dec 13, 2017 3:22 am UTC
Forum: Mathematics
Topic: Bump Function
Replies: 7
Views: 4739

Re: Analytic Bump Function

At x=0, can you prove that your function…
• is continuous?
• is differentiable?
• is twice-differentiable?

What do you imagine a proof that it is infinitely-differentiable would look like?
by Qaanol
Sun Dec 10, 2017 6:33 pm UTC
Forum: Mathematics
Topic: How to prove that End(V) is a k-algebra
Replies: 2
Views: 3049

Re: How to prove that End(V) is a k-algebra

This sounds like homework.

Can you tell us what “k-algebra” means?

Can you tell us what “End(V)” means?

Can you tell us what “Hom(V, V)” means?

Can you tell us what “V” means?
by Qaanol
Tue Dec 05, 2017 2:01 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1976220

Re: Coding: Fleeting Thoughts

Xeio wrote:Todays Google doodle is nice.

They appear to measure “shortest solution” in terms of fewest instructions, not least movement.
by Qaanol
Sat Dec 02, 2017 12:04 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1923: "Felsius"
Replies: 78
Views: 11656

Re: 1923: "Felsius"

chrisjwmartin wrote:
Heimhenge wrote:Why stop with averaging just Celsius and Fahrenheit? Throw Rankine and Kelvin into the mix too. Call it RKCF. I leave the formula as an exercise for the reader.

I hope you're not going to be so timid as to use the arithmetic mean for RKCF.

Obviously it should use the arithmetic-geometric mean.
by Qaanol
Thu Nov 30, 2017 6:35 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 151883

Re: Math: Fleeting Thoughts

↶ One degree is approximately 1.75 percent In what way? It's not 1.75 percent of a circle, or even of a quarter-arc. (Vaguely related, 1px in CSS is about 1.25 arcminutes - the CSS length units are technically angle units, since they scale by viewing distance to subtend the same fraction of your vi...
by Qaanol
Wed Oct 04, 2017 4:21 pm UTC
Forum: Mathematics
Topic: Estimating Max with Only Definite Integrals
Replies: 14
Views: 6220

Re: Estimating Max with Only Definite Integrals

Assuming the sampling rate is significantly higher than the frequencies of the signal, there is indeed an approach that uses a relatively small number of calls to the oracle.
by Qaanol
Mon Oct 02, 2017 7:22 pm UTC
Forum: Mathematics
Topic: Estimating Max with Only Definite Integrals
Replies: 14
Views: 6220

Re: Estimating Max with Only Definite Integrals

Is this for work?

If so, how much is a solution worth to your employer?
by Qaanol
Tue Aug 15, 2017 11:55 pm UTC
Forum: XKCD Meetups
Topic: Maine
Replies: 12
Views: 16111

Re: Maine

CorruptUser wrote:I often go to portland, maine...

Huzzah!
by Qaanol
Thu Jul 13, 2017 3:50 am UTC
Forum: General
Topic: Living in the Wild
Replies: 18
Views: 4638

Re: Living in the Wild

This is a cut-and-paste repost of a thread on this very forum from 2010: link.

Edit: So is the smoking one (albeit with the typo in the subject fixed)

Edit 2: Pretty sure the product/service one is as well: link

Edit 3: And the “intelligent information” one is from 2009: link
by Qaanol
Mon Jun 19, 2017 11:20 pm UTC
Forum: Mathematics
Topic: Approximating distance (alpha-max plus beta-min)
Replies: 0
Views: 5489

Approximating distance (alpha-max plus beta-min)

I’ve been tinkering with the α·max + β·min approximation to the distance formula. As a quick refresher, if you know the x and y distances to some point and want to estimate the straight-line distance, you can take the dot product of ⟨x, y⟩ with an appropriately chosen vector ⟨α, β⟩. Since the dot pr...
by Qaanol
Sun Jun 04, 2017 10:36 pm UTC
Forum: Mathematics
Topic: [Linear Algebra] Finding an orthogonal vector
Replies: 3
Views: 2925

Re: [Linear Algebra] Finding an orthogonal vector

Cauchy wrote:Don't you do that determinant thing that gets you the cross product?

Thank you much!
by Qaanol
Sat Jun 03, 2017 10:24 pm UTC
Forum: Mathematics
Topic: [Linear Algebra] Finding an orthogonal vector
Replies: 3
Views: 2925

[Linear Algebra] Finding an orthogonal vector

Given a basis for a hyperplane in ℝⁿ, what’s the best way to obtain a vector orthogonal to it? In particular, given n independent vectors in ℝⁿ, is there an efficient way to calculate a vector orthogonal to the hyperplane containing all of their differences ( v i − v 0 )? The general problem would b...
by Qaanol
Fri Jun 02, 2017 6:27 pm UTC
Forum: Coding
Topic: Neighbors of a cluster: What is this called?
Replies: 8
Views: 7608

Re: Neighbors of a cluster: What is this called?

As another minor thing, you can improve speed a little by looking at distance^2 rather than distance. The square root operation is one of the slowest basic operations a computer can do. Things often go quite a bit faster if you check whether distance^2<R^2 rather than doing the square root to calcu...

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