Mathematics

Before you roll a die, you could say there is a 1 in 6 chance that it lands on any of the numbered sides. After you roll a die, you could make the point that there is a 1 in 1 chance that it lands on a certain side. I know this is practically irrelevant and too complex for humans to calculate, but it is technically correct. If you were to assign a super-advanced machine to calculate odds, it would always give 1 in 1 odds for it landing on a certain side. It would be able to calculate this from the angle, force, direction etc. of the die throw. If you were to throw the die under the same conditions an infinite numbers of times, the same result would always come up. Th…

I'm going to try for the "Mathematics" forum for this topic but no worries if the mods decide to move this to "The Lounge". I've posted this image which I've described as a "Three-spoke dovetailing tile tessellation". Trispokedovetile tessellation by Peter Dow, on Flickr which is a tessellation of this tile shape, Trispokedovetile by Peter Dow, on Flickr Check my Flickr page for the preceding design iterations and inspiration. I've named the shape Trispokedovetile which is a contraction of "tri-spoke dovetailing tile". "tri-spoke" because the shape is similar to a 3-spoke motorcycle wheel with three bites taken out of it. "dovetailing" because t…

Framework of the idea (1 phrase) In the equality A^n – (C^n – B^n) = AA^(n – 1) – (C – B)R = 0 the number u = A + B – C has k zeros at the end, but the last k + 1 digits in the numbers A^(n – 1) and R one can transform into 00…001, but then the number u = A + B – C has k + 1 zeros at the end. In any case the proof merits of careful analysis. ============ Short PROOF of FLT: If a + b – c = 0 mod(n^k) and a=/ 0 mod(n), then (c – b)^(n – 1) = [(c – b)^n]/(c – b) = a^(n – 1) mod(n^(k+1)) and therefore a + b – c = 0 mod(n^(k+1)) – cf. my Forum: http://www.ivlim.ru/fox/forum/FORUM.asp?FORUM_ID=20&CAT_ID=1&Forum_Title=%C2%E5%EB%E8%EA%E0%FF+%D2%…

I'm reading the book "The rubato music composer" and on fourth chapter, he says i need a basic knowledge about set theory. What are the pre-requisites for learning set theory? And is there a consense of what this basic knowledge may be?

What is the total sum of all numbers? zero?

check here. http://www-groups.dcs.st-and.ac.uk/%7Ehistory/Day_files/Year.html no one famous was born on my birth day. so sad

According to the law of infinite probability, if you were to take a good basketball player and have them shoot 100 free throws an infinite number of times (ignoring fatigue) is it possible for him to eventually miss all 100. I am an assistant coach and had an argument with the head coach over this. Thank you.

What is a tensor and why is it useful? I have grabbed "Vectors, Tensors and the Basic Equations of Fluid Mechanics" by Rutherford Aris, but it is not a gentle introduction (some of the notation used is not explained at all!).

Many years ago, in college, a textbook ordered me to prove that from any point on the directrix, the two tangents that can be drawn to the parabola intersect at a right angle. (Maybe I've got that wrong, but that's how I remember the problem.) I worked on that for months and was never able to solve it, even after the professor told me how to do it. Drove me nuts. So I've never forgotten it. But I've also never found a proof of it. I'd appreciate seeing it proven if anyone cares. But of course I have no right to take anyone's time, so... no obligation or anything. Just something I've been curious about for a long time.

Hello, I found this forum last week while looking for resources to help with my return to college adventure. I am returning to school to finnish my Math Degree after more than 10 years. I droped out of school when my wife was pregnant to find work in the then strong economy. The Dot Com boom was just getting underway at that time and the fruits of my labor were many. However in the down turned economy even after down sizing my families home, vehical, recreation time (no more cable television or movies), my job satisfaction is at an all time low. Realizing that I dont mind living with less I have decided to change careers and become a High school Math Teacher (and h…

To get the inner dimensions right one have to see to it that overblowing produces the overtones in tune and that require one get the tapering right. Could some Math person help me set up the 1732 tapering. suppose the music instrument is 600mm long and the inner tube start as small as 6mm diameter and in the end it is about 30 mm. How is the 1732 related to all the other numbers how does one set it up? I ask because I want to build such an instrument say a Horn in wood or a Sax without mechanics just fingerholes or a oboe without mechanics just fingerholes so would love to get how one set up the equation. I am an old retired person and I have never un…

I heard once of an equation that was proved in a simple way and then the solution was lost. This happened some hundreds of years ago, I think. Does anyone know this equation ? I forgot the exact context.

Hi everyone. Im hoping someone can tell me speed, in MPH, of airflow from an extractor fan please. The extractor is 8inches (200mm) diameter. Figures says its 1600m3/hr. Any help greatly appreciated.

I just created a script that writes any number up to 303 digits long in English: http://www.random.abrahamjoffe.com.au/public/JavaScripts/number_pronunciator.htm Tell me what you think, is it flawed in any way? Like for example: 1001 outputs: "One thousand, and one.", is the comma supposed to be there, and the "and" ?

Hello everyone I have this strange feeling that [math]\frac{(a+b)!}{a!+b!}\in\mathbb{N}[/math]. Can this be proven? If yes, how? Never mind. Counterproof: (15+6)!/(15!+6!) [math]\notin\mathbb{N}[/math]

what do you mean by iota? What is (i)^(1/2)? What is the position of iota in counting dimension? Where is the position of iota

An ant lives on the surface of a cube with edges of length 7cm. It is currentlylocated on an edge x cm from one of its ends. While traveling on the surface of the cube,it has to reach the grain located on the opposite edge (also at a distance xcm from oneof its ends) as shown below. (i) What is the length of the shortest route to the grain if x = 2cm? How many routes ofthis length are there? (ii) Find an x for which there are four distinct shortest length routes to the grain Please tell the steps you have followed to arrive at the solution.

Hello everybody. This is my very first post and I warn you now it's going to be unusual. I have always been a very creative and imaginative person, I have ambitions of becoming an author someday maybe even producing my own animated TV shows. I have always regarded creativity as a realm of infinite possibilities, where anyone and everyone can bring something unique into this world. But lately I been feeling very depressed because of two scientific theories. The first one was introduced to me years ago by my father who has always been very interested in science. He told me that there is a finite limit on the number of books is possible to write. Not because hum…

This is a homework questions I've spent a lot of time trying to solve and I am not sure if I am doing it right. Here is the question: A triangular prism has a base defined by the points (1,3,0), (3,-4,0) and (-2,1,0). The prism has a slant height given by the vector (2,3,7). Determine the volume of this prism. So far I've gotten three answers doing this questions three different ways (using dot product, cross product, cosine law, etc.): 98.43 units3 160 units3 92.14 units3 Can someone please explain to me how I can solve this problem? This is for a gr. 12 calculus and vectors course. Thank you!

The solution of mathematical tasks in the ancient Greek Trisection of angles angle=0° - no solution 180°>angle>0° - general solution (consists of 4 parts) the first part 1.ruler AB 2.ruler AC 3.caliper A-AD 4.ruler DE 5.caliper D-DE 6.caliper E-DE 7.ruler FG intersects DE the point H ,DH=HE 8.caliper H-HE

Dont tell me the answer but how easy is this to do? X = 3 √(X+3)3 - (X+1)3 + (X+8) 3 find X...

I'm assuming this is the proper forum to post this in, even though I'm asking rather than testing whether anyone knows the answer to this (because I don't). Does anyone know how to solve [math]a_{n+1}=e^{a_{n}}[/math] explicitly for [math]a_{n}[/math] in terms of [math]n[/math] and [math]a_{0}[/math]? I would greatly appreciate knowing both the solution and the method used to obtain it, since my own studies have taken me where a solution would be extremely helpful. I haven't been able to determine whether this is a simple textbook equation or a problem entirely unsolved by the mathematical community.

The sentence, "May I draw a round perimeter?" is a mnemonic for remembering the first six digits of pi: Count the number of letters in each word and you get 3.14159. Each of the following phrases is also a mnemonic for pi. Can you figure out HOW each mnemonic stands for 3.14159? Hint: Consider the spelling, sound, and shapes of the words. 1. We won your fun drive sign. 2. Circles and diameters are equally important. 3. The easy vowels echo mathematical magnitude. 4. Bring in your initial six questions. Good luck. Note: The world record for the most digits of pi memorized is now over 40,000 digits. The record holder used very sophisticated mnemoni…

What is the difference between mathematical laws, such as the law of sines/cosines/tangents, exponents. logarithms, etc. and mathematical theorems (the binomial theorem, fundamental theorem of calculus, and pythagorean theorem). Do theorems ever eventually become laws or how is it decided if something is a law or theorem?

I realized something the other day. Almost every three-dimensional shape we know of - cube, cone, cylinder, prisms, etc - can be formed simply by extending their two-dimensional equivalents - square, circle, trapezoid, etc. - into the third dimension; in other words by being given depth. There are several that this doesn't really apply for such as the square based pyramid, but that is a combination of the square and triangular-faced cone. The sphere however is different; because technically it has no two dimensional equivalent, most would say that the circle is the 2d sphere, but in reality the circle is a 2d cylinder, since if you give a circle depth, it becomes a cy…