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Dan's user avatar
Dan's user avatar
Dan
  • Member for 7 years, 5 months
  • Last seen this week
32 votes

Coin Flip Probability Independent or Not?

22 votes
Accepted

If $(a,b,c)$ are the sides of a triangle, what is the probability that $ac>b^2$?

17 votes
Accepted

Incorrect partial sum formula in textbook?

13 votes

Five circles in a rectangle: can the circles move?

12 votes

What are some conjectures of your own?

12 votes

Roll a dice infinitely many times, what is the probability of getting a 5 before a 6

11 votes
Accepted

Prove/Disprove $|1 + z_1| + |1 + z_2| + |1 + r z_1 z_2| \ge 1 + \min(r, 1/r)$

10 votes

Mathematical coincidences concerning the numbers $\pi$, $e$ and $163$

9 votes
Accepted

Help needed in finding the area of the square (tricky geometry question)

8 votes
Accepted

In Pascal's triangle without the $1$s, what is the sum of squares of reciprocals?

8 votes

The golden ratio in a parabola

8 votes

Break a stick at two random points. The probability that the longest piece is at least twice as long as each of the other pieces is $1/2$. Why?

8 votes

Is the smallest root of a polynomial always complex if the coefficients is the sequence of prime numbers?

7 votes

A curious coincidence: $\prod\limits_{k=1}^\infty\left(1+\int_{k}^{k+1}\left(\frac{\sin (\pi x)}{x}\right)^2\mathrm dx\right)\overset{?}{=}\pi/2$

7 votes
Accepted

Showing that, in Pascal's triangle, the product of the numbers along each median is always the same.

7 votes

Why does a circle appear when we square a polynomial whose inflection points are all on the $x$-axis?

7 votes

Position of crease-point on right edge of $40\times40$ square upon folding top-left corner to midpoint of bottom edge?

6 votes

Evaluate the indefinite integral $\int\frac{dx}{(x^2+1)\sqrt{x^2+1}}$ without trigonometric substitution.

6 votes
Accepted

A triangle has one vertex at a circle's center and two vertices on the circle. Can the three enclosed regions have rational areas?

6 votes

$\int_0^{\pi/2}\int_0^{\pi/2}\frac{(\tan\alpha)(\tan\beta)}{\tan\alpha+\tan\beta} d\alpha d\beta=(0.9999999913...)(\pi/2)$? Seriously?

6 votes
Accepted

Probability that two random lines intersect inside a square

6 votes
Accepted

Distances of Fermat point from vertices of a triangle

6 votes

Definite integral of infinite product

5 votes

Prove or disprove: There is a way to choose independent random chords in a circle so that their intersections are uniformly distributed in the circle.

5 votes

The sum of the squares of the diagonals in a polygon

5 votes

Draw tangents at 3 random points on a circle to form a triangle. Show that the probability that a random side is shorter than the diameter is $1/2$.

5 votes
Accepted

Find the minimum value of $~\cos(x)~$,if $\cos(x) + \cos(y) +\cos(z)=1$ and $\sin(x) + \sin(y)+\sin(z)=1$ for x,y,z being real numbers.

5 votes

Find The Locus of the Triangle When the Difference of Its Base Angles are Given

5 votes
Accepted

What is a closed form of this limit? (product of areas in circle with parabolas)

4 votes

Expected value of repeatedly betting on a coin flip?

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