Dan
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 Feb13 answered Expressing numbers in cartesian form Feb13 asked How much advantage would a Blackjack player gain by being able to see the underside of cards? Jan22 comment How do I convince my students that the choice of variable of integration is irrelevant? If you want to mess with students' heads, use $e$ as a variable of integration. Jan21 comment If $5 \times 12 = 104$, how much is $10 \times 11$? It also works if the base is equal to 2. Dec24 comment Why every prime (>3) is represented as $6k\pm1$ This sieve of "potentially prime" numbers will include all the primes (except for a finite number of small primes which are divisors of $m$), but will also include some "false positives" that aren't actually prime. We want the sieve to be as small as possible in order to minimize these "false positives". Dec24 comment Why every prime (>3) is represented as $6k\pm1$ For any given value of $m$, there are some numbers $n$ that can be trivially shown to be composite based only on the value of $n$ mod $m$ (or equivalently, the last digit when $n$ is written in base $m$). I call all the other natural numbers "potentially prime". For example, in familiar base-ten, the numbers 90, 92, 94, 95, 96, and 98 can be ruled out as prime based solely on their last digit. The numbers 91, 93, 97, and 99 are "potentially prime" based on their last digit, even though 97 is the only one that's really a prime. Dec23 answered Why every prime (>3) is represented as $6k\pm1$ Dec19 comment Prove that this number is irrational $a = 0.124578912456891245689123568912356890235679023567902346790234679013467801346780‌​134578013457801245780...$ Dec16 comment Prove the lecturer is a liar… As the number of attendees approaches infinity, $b/a$ approaches $\sqrt[3]{3} - 1$. Dec16 comment Prove the lecturer is a liar… Some small approximate solutions are (8, 3) with a probability of 56/165, and (10, 4) with a probability of 30/91. Dec16 answered Prove the lecturer is a liar… Dec13 comment Travelling to the point of origin without using the same road twice Note that's it's not true if there are only $n-1$ roads. (For example, consider 5 cities connected with 4 roads in an X-shaped graph.) What is it about adding the nth road that forces there to be a cycle? Dec12 answered Why does Trapezoidal Rule have potential error greater than Midpoint? Dec9 answered Help with standard deviation and probability Dec7 awarded Custodian Dec7 reviewed Approve Area of a square in polar coordinates? Dec7 answered Area of a square in polar coordinates? Dec7 answered Which is the impossible voting in election? Dec3 answered How to prove that either $2^{500} + 15$ or $2^{500} + 16$ isn't a perfect square? Dec2 comment Proof that every circle has the ratio of $\pi$ @Omnomnomnom: A circle is the set of all points in a plane that are a given distance (called the radius) away from a given point (the center).