eta oin shrdlu wrote:Maybe Jörg Arndt's arctan page?

Yes! That’s the one, thanks!

- Fri May 31, 2019 8:01 pm UTC
- Forum: Mathematics
- Topic: Help finding an arccotan website
- Replies:
**3** - Views:
**880**

eta oin shrdlu wrote:Maybe Jörg Arndt's arctan page?

Yes! That’s the one, thanks!

- Fri May 31, 2019 3:00 am UTC
- Forum: Mathematics
- Topic: Help finding an arccotan website
- Replies:
**3** - Views:
**880**

I remember visiting a website which I cannot seem to locate anymore. It had an extensive list of Machin-like formulas, organized by number of terms. It was mostly plain-text, and used the notation [n] for arccotan(n). It also included formulas with half-integer arguments, as [n/2]. I believe there w...

- Sun Apr 21, 2019 12:18 pm UTC
- Forum: Mathematics
- Topic: Show that a triangle is right angled
- Replies:
**2** - Views:
**1241**

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

Try drawing a picture.

Is this homework?

Try drawing a picture.

Is this homework?

- Mon Apr 01, 2019 4:48 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2131: “Emojidome”
- Replies:
**123** - Views:
**20433**

https://imgs.xkcd.com/comics/emojidome.png https://xkcd.com/2131/ Alt-text: “🤼🤼🤼🤼🤼🤼🤼🤼” (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 ...

- Thu Feb 28, 2019 4:04 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 2117: "Differentiation and Integration"
- Replies:
**45** - Views:
**8299**

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...

- Sat Feb 09, 2019 8:38 pm UTC
- Forum: Mathematics
- Topic: The frog riddle
- Replies:
**23** - Views:
**5661**

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 ...

- Tue Feb 05, 2019 1:19 am UTC
- Forum: Mathematics
- Topic: The frog riddle
- Replies:
**23** - Views:
**5661**

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.

- Sat Jan 12, 2019 8:05 am UTC
- Forum: Mathematics
- Topic: Math: Fleeting Thoughts
- Replies:
**434** - Views:
**159205**

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...

- Thu Jan 10, 2019 9:48 pm UTC
- Forum: Mathematics
- Topic: Favorite Mathematical Equation
- Replies:
**87** - Views:
**20888**

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.

- Thu Nov 01, 2018 5:03 pm UTC
- Forum: Mathematics
- Topic: How to find confidence interval for vector-valued function?
- Replies:
**5** - Views:
**3591**

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 (x_{0}) of the reagent was added.

- Wed Oct 31, 2018 11:51 pm UTC
- Forum: Mathematics
- Topic: How to find confidence interval for vector-valued function?
- Replies:
**5** - Views:
**3591**

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...

- 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:
**3520**

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...

- 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:
**7165**

I believe this is a linear programming problem—very nearly a textbook example of one—and as such can be solved in polynomial time.

- Sun Jul 01, 2018 9:54 pm UTC
- Forum: Language/Linguistics
- Topic: Oxford comma query
- Replies:
**28** - Views:
**12040**

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...

- Mon May 07, 2018 6:19 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1990: "Driving Cars"
- Replies:
**86** - Views:
**15022**

Why is there a ghost behind Cueball?

- Mon Apr 16, 2018 10:18 pm UTC
- Forum: Mathematics
- Topic: Projecting a Polytope
- Replies:
**5** - Views:
**4990**

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...

- Mon Apr 16, 2018 4:24 pm UTC
- Forum: Mathematics
- Topic: Projecting a Polytope
- Replies:
**5** - Views:
**4990**

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.

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.

- Fri Apr 06, 2018 9:20 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1977: "Paperwork"
- Replies:
**7** - Views:
**3755**

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.

- Mon Apr 02, 2018 9:02 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1975: "Right Click"
- Replies:
**42** - Views:
**20957**

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.”

- Mon Apr 02, 2018 8:13 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1975: "Right Click"
- Replies:
**42** - Views:
**20957**

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 ...

- Tue Mar 20, 2018 11:07 pm UTC
- Forum: Mathematics
- Topic: A probability question
- Replies:
**5** - Views:
**5161**

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...

- Tue Mar 20, 2018 8:56 pm UTC
- Forum: Mathematics
- Topic: A probability question
- Replies:
**5** - Views:
**5161**

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.

The *actual* results are consistently close to 83.1% for H = J, and 6.4% for H = L.

- Sun Mar 18, 2018 6:43 am UTC
- Forum: Mathematics
- Topic: A probability question
- Replies:
**5** - Views:
**5161**

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 ...

- Fri Mar 16, 2018 8:50 pm UTC
- Forum: Computer Science
- Topic: Looking for an algorithm to test for abridgement
- Replies:
**3** - Views:
**4850**

- Fri Mar 16, 2018 4:22 am UTC
- Forum: Computer Science
- Topic: Looking for an algorithm to test for abridgement
- Replies:
**3** - Views:
**4850**

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...

- Fri Feb 02, 2018 4:07 pm UTC
- Forum: Mathematics
- Topic: Mathematics of p-hacking: random walks and significance
- Replies:
**9** - Views:
**7364**

>-) 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.

- Tue Jan 30, 2018 11:56 pm UTC
- Forum: Mathematics
- Topic: Mathematics of p-hacking: random walks and significance
- Replies:
**9** - Views:
**7364**

>-) 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.

- Mon Jan 15, 2018 9:13 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1942: “Memorable Quotes”
- Replies:
**37** - Views:
**9731**

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...

- Fri Dec 15, 2017 5:47 am UTC
- Forum: Mathematics
- Topic: Bump Function
- Replies:
**7** - Views:
**4929**

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 ...

- Wed Dec 13, 2017 3:22 am UTC
- Forum: Mathematics
- Topic: Bump Function
- Replies:
**7** - Views:
**4929**

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?

• is continuous?

• is differentiable?

• is twice-differentiable?

What do you imagine a proof that it is infinitely-differentiable would look like?

- Sun Dec 10, 2017 6:33 pm UTC
- Forum: Mathematics
- Topic: How to prove that End(V) is a k-algebra
- Replies:
**2** - Views:
**3156**

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?

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?

- Tue Dec 05, 2017 2:01 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9990** - Views:
**2007566**

Xeio wrote:Todays Google doodle is nice.

They appear to measure “shortest solution” in terms of fewest instructions, not least movement.

- Sat Dec 02, 2017 12:04 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1923: "Felsius"
- Replies:
**78** - Views:
**12426**

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.

- Thu Nov 30, 2017 6:35 am UTC
- Forum: Mathematics
- Topic: Math: Fleeting Thoughts
- Replies:
**434** - Views:
**159205**

↶ 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...

- Wed Oct 04, 2017 4:21 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**6491**

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.

- Mon Oct 02, 2017 7:22 pm UTC
- Forum: Mathematics
- Topic: Estimating Max with Only Definite Integrals
- Replies:
**14** - Views:
**6491**

Is this for work?

If so, how much is a solution worth to your employer?

If so, how much is a solution worth to your employer?

- Tue Aug 15, 2017 11:55 pm UTC
- Forum: XKCD Meetups
- Topic: Maine
- Replies:
**12** - Views:
**16712**

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

Huzzah!

- Thu Jul 13, 2017 3:50 am UTC
- Forum: General
- Topic: Living in the Wild
- Replies:
**18** - Views:
**4861**

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

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

- Mon Jun 19, 2017 11:20 pm UTC
- Forum: Mathematics
- Topic: Approximating distance (alpha-max plus beta-min)
- Replies:
**0** - Views:
**5601**

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...

- Sun Jun 04, 2017 10:36 pm UTC
- Forum: Mathematics
- Topic: [Linear Algebra] Finding an orthogonal vector
- Replies:
**3** - Views:
**3029**

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

Thank you much!