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Nick's user avatar
Nick
  • Member for 11 years, 2 months
  • Last seen more than a week ago
  • K-PAX
100 votes
18 answers
22k views

Can the golden ratio accurately be expressed in terms of $e$ and $\pi$

54 votes
3 answers
4k views

Sheldon Cooper Primes

39 votes
16 answers
106k views

Prove $\sin^2\theta + \cos^2\theta = 1$

23 votes
4 answers
5k views

Given two blank rulers, measure any length

22 votes
6 answers
35k views

Approximating Logs and Antilogs by hand

19 votes
5 answers
6k views

Do equal bases imply equal powers?

18 votes
3 answers
808 views

Evaluate $\int_0^{\pi/2} \frac{\ln\left(e^{2x} + 1\right)}{1 + \sin2x}\mathrm dx$

15 votes
3 answers
87k views

If the sum $\frac{1}{7} + \frac{1\cdot 3}{7\cdot 9} + \frac{1\cdot 3\cdot 5}{7\cdot 9\cdot 11} + ...$ to 20 terms is $\frac{m}{n}$, then $n-4m$?

12 votes
8 answers
658 views

Avoiding the Integration Constant

11 votes
5 answers
541 views

Prove $3(\sin x-\cos x)^4 + 6(\sin x+ \cos x)^2 + 4(\sin^6 x + \cos^6 x) -13 = 0$

10 votes
4 answers
32k views

What are the conditions for a polygon to be tessellated?

9 votes
3 answers
5k views

Explaining Hypercomplex numbers to Children.

8 votes
1 answer
669 views

$\frac{x}{10!} = \frac{1}{8!} + \frac{1}{9!}$

8 votes
4 answers
586 views

Finding $\frac{\mathrm d}{\mathrm dx} x!$

7 votes
2 answers
564 views

Is there a latus other than the one in the rectum?

6 votes
8 answers
16k views

Why does the Denominator of the Denominator go to the Numerator?

6 votes
3 answers
295 views

$1 + \frac{1}{1+2}+ \frac{1}{1+2+3}+ ... + \frac{1}{1+2+3+...+n} = ?$

6 votes
6 answers
7k views

Why is 11 times the 7th term of a fibonacci series equal to the sum of 10 terms?

6 votes
0 answers
189 views

How must have Liu Xin calculated $\pi$?

5 votes
2 answers
1k views

Prove $\lim_{x \to 0} \frac{e^{\sin(x)} - e^{\tan (x)}}{e^{\sin (2x)}-e^{\tan (2x)}} = \frac{1}{8}$

5 votes
1 answer
308 views

Why can't we generalize straight line equations for all curves?

5 votes
1 answer
1k views

Evaluate $\int \ln(1 + e^x)\ \mathrm dx$

4 votes
1 answer
196 views

Maximize $Z=-x+2y$ given $x\geq 3,\ x+y\geq 5,\ x+2y\geq 6,\ y\geq 0$

4 votes
2 answers
82 views

Calculation of $\lim\limits_{x \to 0} \frac{\frac{\mathrm d}{\mathrm d x} (e^{\sec x})}{\frac{\mathrm d}{\mathrm d x} (e^{\sec 2x})}$

4 votes
2 answers
175 views

Is $x = 2$ is the only real solution for $a^x + b^x = c^x$ when $(a,b,c)$ is a pythagorean triplet?

4 votes
0 answers
90 views

An Easier way to solve simple equations of this type

4 votes
4 answers
1k views

Explaining multiplication of fractions

4 votes
2 answers
135 views

$2 \uparrow^n 2 = 4$ and the magnificence of $2$

4 votes
1 answer
7k views

Can Pi prod be expressed using Sigma Notation?

3 votes
5 answers
335 views

$2 - 4 + 6 - 8 + \cdots = 1 - 1 + 1 -1 + \cdots$?