Nerd Paradise : Divisibility Rules for Arbitrary Divisors It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0. The number is both divisible by 2 and divisible by 3. Cut the number into 2 parts: the last digit and everything else before that. The last 3 digits are divisible by 8 The sum of all the digits in the number is divisible by 9. The last digit is a 0. Break the number into two parts (like you did for the division by 7 rule). Also there is a quick way for determining divisibility by 11 for 3-digit numbers: If the inner digit is larger than the two outer digits, then it is divisible by 11 if the inner digit is the sum of the two outer digits. Rules for all divisors ending in 1... User Comments: 9 Dividing By 12
Brain Explorer 6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D. R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. 9990 – 0999 = 8991 (rather than 999 – 999 = 0) 9831 reaches 6174 after 7 iterations: 8820 – 0288 = 8532 (rather than 882 – 288 = 594) 8774, 8477, 8747, 7748, 7487, 7847, 7784, 4877, 4787, and 4778 reach 6174 after 4 iterations: Note that in each iteration of Kaprekar's routine, the two numbers being subtracted one from the other have the same digit sum and hence the same remainder modulo 9. Sequence of Kaprekar transformations ending in 6174 Sequence of three digit Kaprekar transformations ending in 495 Kaprekar number Bowley, Rover. "6174 is Kaprekar's Constant".
Weierstrass functions Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x. Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr.
Role Playing Games - Free Multiplayer Online Games Astro Lords is an MMORPG/Strategy set in a sci-fi universe. Players control an asteroid, construct and upgrade buildings and fight with others to gain control over the Oort cloud. The game can be played on iOS, Android and desktop devices. Players might be positively appalled by the lack of character customization, but that is more than compensated by the fact that eventually you can move your base, perhaps towards the members of your alliance, or the enemy if you feel you can gain an edge. The combat has players duke it out in turn-based combat with spaceships in the vast void. It takes quite some skill and provides ample entertainment, because the fights involve dodging slow-moving projectiles (there are lasers too!) Astro Lords is definitely a promising title, but the strategy elements could very well be executed better. See Videos Free, with option to pay for additional features. Play Astro Lords now!
Online Speed Reading tools and software Simply start by clicking on the Play button on the left. Reading is that one activity that we do every day but we don't really practice. Most people learn the basics of reading in kindergarten and never graduate to the next levels. You are probably using the same basic rudimental tools and techniques that you learned when you were 6. The average American person reads at an average speed of 180 to 240 words per minute and has done so since he was 16 years old. Does it make sense that we hit our best performance at age 16 and that we don't improve much after that? Keep in mind less than 10% read at 400 words per minute and less than 1% faster than 600. Have you ever wished you could take one of those costly speed reading courses? The problem with those courses is that you have to keep practicing those techniques until they become second nature. That's the goal of this site. We are here to keep you focused and to help you improve your speed reading everyday. What is sub-vocalization?
- StumbleUpon The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of sides is The total length of the spiral for an -gon with side length is therefore Consider the solid region obtained by filling in subsequent triangles which the spiral encloses. -gons of side length , is The shaded triangular polygonal spiral is a rep-4-tile. Cranial Nerves Can't remember the names of the cranial nerves? Here is a handy-dandy mnemonic for you: On Old Olympus Towering Top AFamous Vocal German Viewed Some Hops. The bold letters stand for: olfactory, optic, oculomotor, trochlear, trigeminal, abducens, facial, vestibulocochlear, glossopharyngeal, vagus, spinal accessory, hypoglossal. Still can't remember the cranial nerves?
Nerd Paradise : Calculating Base 10 Logarithms in Your Head Calculating base 10 logarithms in your head on the fly is a lot easier than you may think. It is simply a matter of memorization and a little estimation... First memorize all the single digit base 10 logs. Don't worry, it's not as painful as it sounds. I even made the chart for you: Remember this rule from high school? And what about this one, you remember it too? Good. Example #1: base 10 log of 400 That's the same thing as log(4*100) which equals log 4 + log 100. log of 4 you know from the table above. Now you may ask, what if it isn't just a number with a bunch of 0's after it? Example #2: base 10 log of 35 Suppose you wanted to find the logarithm of 35. Our guess: 1.545 Calculator says: 1.544068... Now you can convince all your friends and teachers that you are autistic. Example #3: base 10 log of 290438572: This is fairly close to log(2.9 * 100000000) = log 2.9 + log 108 2.9 is close to 3. Our Guess: 8 + .45 = 8.45 Calculated Answer: 8.46305... User Comments: 14 And so it goes. To recap: Fixed.
Your Age On Other Worlds Want to melt those years away? Travel to an outer planet! <div class="js-required"><hr> This Page requires a Javascript capable browser <hr></div> Fill in your birthdate below in the space indicated. The Days (And Years) Of Our Lives Looking at the numbers above, you'll immediately notice that you are different ages on the different planets. The earth is in motion. The top-like rotation of the earth on its axis is how we define the day. The revolution of the earth around the sun is how we define the year. We all learn in grade school that the planets move at differing rates around the sun. Why the huge differences in periods? Johannes Kepler Tycho Brahe Kepler briefly worked with the great Danish observational astronomer, Tycho Brahe. Here you see a planet in a very elliptical orbit. Kepler's third law is the one that interests us the most. Let's just solve for the period by taking the square root of both sides: The Gravity Of The Situation Isaac Newton ©2000 Ron Hipschman