Unsolved Problems. 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.
HeartCurves_801.gif (GIF-bilde, 455x306 punkter) BBP Formula. Factorion. Fibonacci Number. The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation with .
As a result of the definition (1), it is conventional to define The Fibonacci numbers for , 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... Epicycloid. The path traced out by a point on the edge of a circle of radius rolling on the outside of a circle of radius .
An epicycloid is therefore an epitrochoid with . A polar equation can be derived by computing so. Triangle Dissection Paradox. Dual Tessellation. Two Trains Puzzle. Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h.
A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains? Now, the trains take one hour to collide (their relative speed is 100 km/h and they are 100 km apart initially). Prime Spiral. The prime spiral, also known as Ulam's spiral, is a plot in which the positive integers are arranged in a spiral (left figure), with primes indicated in some way along the spiral.
In the right plot above, primes are indicated in red and composites are indicated in yellow. The plot above shows a larger part of the spiral in which the primes are shown as dots. Unexpected patterns of diagonal lines are apparent in such a plot, as illustrated in the above grid. This construction was first made by Polish-American mathematician Stanislaw Ulam (1909-1986) in 1963 while doodling during a boring talk at a scientific meeting. Remarkably, noted science fiction author Arthur C. However, Clarke never actually performed this thought experiment (pers. comm. to E. M. A hexagonal prime spiral can also be constructed, as illustrated above (Abbott 2005). What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree. Clever student: I know!
Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step. Which is true since anything times 0 is 0. Cleverest student : That doesn’t work either, because if then. Math for Artists: Exponents and Radicals. The Tesseract. Cgi-bin Matrix Solver. Solving a linear equation system of up to 20 unknowns.
If you need some help please scroll down to the example. If not, fill the 2 boxes below , then click on the "Go" button. Example As an example, let's say you have the following 3 equations to solve for the unknowns x , y , and z : 2x + 3y + 1/3z = 10 3x + 4y + 1z = 17 2y + 7z = 46. Doublepe.gif (GIF-bilde, 268x223 punkter) Mathematica Online Integrator. K-MODDL > Tutorials > Reuleaux Triangle. If an enormously heavy object has to be moved from one spot to another, it may not be practical to move it on wheels.
Instead the object is placed on a flat platform that in turn rests on cylindrical rollers (Figure 1). As the platform is pushed forward, the rollers left behind are picked up and put down in front. An object moved this way over a flat horizontal surface does not bob up and down as it rolls along. The reason is that cylindrical rollers have a circular cross section, and a circle is closed curve "with constant width. " What does that mean? Is a circle the only curve with constant width? How to construct a Reuleaux triangle To construct a Reuleaux triangle begin with an equilateral triangle of side s, and then replace each side by a circular arc with the other two original sides as radii (Figure 4). 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. (Leading zeros are allowed.)Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2. 9990 – 0999 = 8991 (rather than 999 – 999 = 0) 9831 reaches 6174 after 7 iterations: 8820 – 0288 = 8532 (rather than 882 – 288 = 594)