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Apr
15
answered Using the slope from part (b), what is the equation of the tangent line to the curve at P?
Jan
7
revised Stuck on integrating $\int x/(1-x)dx$
edited body
Jan
7
revised Stuck on integrating $\int x/(1-x)dx$
typesetting
Jan
7
suggested approved edit on Stuck on integrating $\int x/(1-x)dx$
Jan
7
answered Stuck on integrating $\int x/(1-x)dx$
Dec
28
comment How to show that show that $\frac{v+u}{1+ uv/c^2}=c$ when $u=c$?
I'm guessing that you really mean $(u+v)/(1 + \frac{uv}{c^2})$, not $u+\left(v/(1 + \frac{uv}{c^2})\right)$.
Dec
28
answered Why is $\cos(x/2)+2\sin(x/2)=\sqrt5 \sin(x/2+\tan^{-1}(1/2))$ true?
Dec
26
answered Reference request: self-contained rigorous introductions to “cool” topics
Dec
22
awarded  Critic
Dec
19
comment Finding the points of intersection of a circle and a line
In Exercise 2, your two points do not satisfy $x + y - 1 = 0$.
Dec
5
comment What is a simple example of an unprovable statement?
Do you have a reference to this problem or Erdős's paper? 5 minutes of Googling didn't turn it up, but that may be because your (nice) presentation of it isn't the canonical one.
Oct
5
comment Expected deviation of a coin that obeys the gambler's fallacy
My attempt to prove via induction that the variance is $\frac n {12}$ continues but is kind of in the weeds. Having that closed form of the probability of $h$ heads after $n$ flips couldn't hurt. The recurrence given on the Wikipedia page bears enough resemblance to the formula for $H(n)$ that I assume a proof that the probabilities are actually Eulerian is straightforward.
Sep
30
comment Expected deviation of a coin that obeys the gambler's fallacy
Calculation "by hand" (with a Python program) indicates that for $n \ge 3$, the variance is $\frac{n}{12}$ so the standard deviation is $\frac{1}{2\sqrt3}\sqrt n$. If I'm able to prove it (induction seems promising), I'll add the proof as an answer.
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Aug
27
comment A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white.
If the book calls it "Baye's Theorem", I would not trust the book.
Aug
5
revised Refining my knowledge of the imaginary number
Corrected Chris Culter's anme
Jun
4
comment 'Obvious' theorems that are actually false
You order the rationals $q_1, q_2, \ldots, q_n, \ldots$ and place an interval of $(\frac \epsilon 2)^n$ around each one, choosing $\epsilon$ to be less than $1$.
May
23
comment Are mathematical articles on Wikipedia reliable?
I was curious whether Nature had a response to the response, and they did, here and here. (I have no contribution to make regarding which side is in the right; I'm just presenting the documents for others who are curious).
May
1
comment Examples of mathematical results discovered “late”
It took a surprisingly long time (17th century) for even very basic concepts of probability theory to be developed, considering that those concepts would have been immensely valuable in real life, given that gambling has been popular forever.