Mathematics

Is 1+1 always 2? I tried to prove that 1+1 is not always 2 with applying Goedel's incompleteness theorem as; http://hecoaustralia.fortunecity.com/incompleteness/incomplete.htm

Is the only reason that our mathematics are 10 based because we he 10 fingers and the first calculator was only our fingers ?

Hi, I am 100% new to all of these boards. I have been drawn here because I saw a science forum, and inside of that an astronomy and cosmology forum (!). I thought it would be better to ask here, and not in science for my question about scientific notation. I remember learning about this, a long time ago, but I have forgotten, and need help. =\ Is there any easy way (minus using a calculator) to solve equations such as 26^78 or 13^90 and so on? I'm just making up these numbers at random, so please be gentle. I appreciate any help!

Consider this riddle. The result it claims is fairly remarkable, and yet the solution, although a bit difficult to digest at first, is logically sound, but based on axiom of choice. Just sharing it because I think it is really cool, and I figure this community would enjoy.

Actually my problem is to find my proof that there are an infinite number of solutions to the Diophantine equation 5a^2 + 5ab + b^2 = p^n where a,b are coprime and p is a prime ending in 1 or 9. There is a relationship between any three consecutive term of a Fibonacci type series and the form 5a^2 + 5ab + b^2 that is invariant with the index number of the first term. That is a key to my proof. I leave the proof for you to figure out, but will make suggestions if you reach a dead end and have no idea where to turn. First off then, how does the form 5a^2 + 5ab + b^2 relate to three terms of a Fibonacci type series in an invariant manner? (By Fibonacci type, I mean F(n…

In the process of a patent/copyright research I happened upon a copyrighted 12-tone Scientific Scale. Don't know what the application of it might be, bu do know that the 7-tone Scientific Scale of Pythagoras is the standstill to mathematics in the Western world. In any event I copied it down to give here should there be the interest: 12-tone Scientific Scale: F#= 1.4046639.... C= 2.0 (fundamental) C#= 1.0534979.... G= 1.5 G#= 1.5802469.... D= 1.125 D#= 1.1851851.... A= 1.6875 A#= 1.7777777.... E= 1.265625 F = 1.3333333.... B= 1.8984375 Do not confuse the scale with ton…

Perfect squares end in 1,4,5,6,9 and zero. Nice symmetry. Especially with the squares of 1 & 9 (5 +/- 4) ending in 1 2 & 8 (5 +/- 3) ending in 4 5 (5 +/- 0) ending in 5 4 & 6 (5 +/- 1) ending in 6 3 & 7 (5 +/- 2) ending in 9 WHAT ABOUT SQUARE ENDINGS? 100, 400, 900, 1600; of course, if a number ends with a zero, its square ends in 00 Is the only other repeated end for a square 44? 144 1444 3844 7744 12544 19044 26244 35344 44944 56644 68644 are all perfect squares their square roots are (50n +/-12)2 and n = 0,1,2 . . . For further amusement, 213,444 = 4622, and is the second member …

I was reading about the Arecibo message thingy, with the message being transmitted in 1679 bits because there's only two ways to lay out 1679 in a grid, one of which would make "sense" and one that wouldn't. Then I thought, this would only work if aliens used a square grid system (where information can have x & y co-ordinates) for their layouts, which there's no guarantee they would... What if alien visual representations or data were laid out on a hex grid? Maybe they would arrange them from the center spiraling outwards either clockwise or counter-clockwise. Maybe they would be arranged in rows and zigzag columns, or columns and zigzag rows, or maybe …

When does 1 and 1 make 3? Happy New Year

Does anybody else find this fascinating--that if both operands are 2 for any "growth" operator, then the result will always be 4. By a "growth" operator, I mean +, x, power, etc.--and operation whose result is greater than its operands (as opposed to "shrinking" operators like -, /, square root, etc.). 2 + 2 = 4 2 x 2 = 4 2 ^ 2 = 4 2 # 2 = 4 (where we could suppose x # y means x raised to itself y times). Wouldn't this trend go on indefinitely? Couldn't we say that 2 @ 2 = 4 where @ is any "growth" operator whatever? And wouldn't a similar rule apply where 4 % 2 = 2 where % is any "shrinking" operator whatever? NOTE: I'm aware that I've defined "growth"…

Here is a strange equation I found: a=b a^2 = ab a^2 - b^2 = ab - b^2 (a + b)(a - b) = b(a - b) a + b = b (a = b) a + a = a 2a = a 2 = 1 This still works, even if you substitute "a" and "b". 2 = 2 2^2 = 2(2) 2^2 - 2^2 = 2(2) - 2^2 (2 + 2)(2 - 2) = 2(2 - 2) 2 + 2 = 2 4 = 2

Hello everyone I have 2 questions: First of all, I'd like to know if these (notations) are correct: [math]\left(u_n=\sum_{i=0}^{+\infty}{10^i}\right)\equiv (1,0,1,0,1,0,\cdots )\bmod11[/math] [math]\left(u_n=\sum_{i=0}^{+\infty}{10^i}\right)^2\equiv (1,0,1,0,1,0,\cdots )\bmod11[/math] Secondly and finally, I'd like to know if it's possible to prove that the row [math]\left(u_n=\sum_{i=0}^{+\infty}{10^i}\right)=(1,11,111,1111,11111,111111,\cdots)[/math] has no prime numbers in it (11 excluded)? Thank you! -Function P.S. Could the title please be changed to "2 characteristics of the row (1, 11, 111, 1 111, ...)"? Thanks.

Why 2 multiply 2 is equal 4?proof?

Two identical ships next to each other in the middle of a river heading against the current; one at full throttle developing 1000 horsepower just counteracts the current and does not advance at all. The other is anchored. How many horsepower does the anchor produce ?

Hello, everyone! Can you explain me what can we measure in 4 dimensional space? If, in 2d - Area, 3d - volume.... Thank you!

suggestion : 2r is diagonal of square inside the oval

Greetings: I am a first time user of this web site, so, Imay make a few mistakes. I want to re-learn the formula for determining the diagonal distance between the ends of a 3-4-5 right triangle. The the known measurements are 10 ft and 12 ft.

It is probably a too long of title, but this question loomed in my mind. We all know that 3 dimensional geometric volumes have a finite size(unless told otherwise), and 2 dimensional shapes are made up of lines that are infinitely thin. However, 3 dimensional volumes such as cylinders are made up(theoretically) of 2 dimensional circles that are stacked upon each other until a given height, yet 2 dimensional shapes with lines that are infinitely thin are able to make up a certain height. How is this possible? I mean the formulas for determining surface area and volume are based on these principles, though I could be wrong.

Its the last round of a game show. You have to choose between three doors labeled One, Two, and Three. Behind each door is a prize. Now two of the doors contain goats while one of the doors contains a brand new car. Your asked to choose a door number. Lets say you choose 1. The Host then reveals a door other than the one that you choose, lets say that it is door number 3, and it has a goat behind it. You are then asked if you would like to change your choice to number 2 or stick with number 1. Now the riddle is, does this make a difference? Should you change your answer or stick with it? Have you all heard of this wierd puzzle? I have a book about it, but t…

Hi, I have two points in 3D space: point A: (1,2,3) point B: (4,7,6) I want to find a third point between the two, where z = 5 So, point C: (x,y,5) How can I calculate x and y for point C. Thanks.

Trying to setup 3D Math right in svg here's how far I have gotten. The Z axis is obviously a translation on the x and y co-ordinates. At the moment I am using a translation of 1 but I am wondering would it be right to use the square root of 0.5? <script> function Three_Dimensional_Resolve_Points(matrix){ var svg = {width:800, height: 800}, midpoint = {x:svg.width/2, y:svg.height/2}; Z_Translate = {X : -1, Y : 1} X = matrix[0] + (matrix[2]*Z_Translate.X) + midpoint.x; Y = matrix[1] + (matrix[2]*Z_Translate.Y) + midpoint.y; return [X,Y]; } svg = { width : 800, …

I need a formula to calculate all three coordinates a third point of a triangle. Here is a sketch of a random triangle just so it makes it easyers for me to explain my problem: TRIANGLE I have x,y and z of points A and B, and lenght all of the sides (a,b and c) The third point, C, must be between A and B in x-z axises (that should reduce the solutions from a circle (actualy the edge of a circle, i dont know the english term) to only 2 points), and I only need the point that is above the line c on y axis. I could calculate that manualy, but i need a formula that works allways becouse i need it for the movement of my robot (it isnt homework, just a project =…

a friend of mine said there was a way to prove 4 is more than 5 could anyone please explain?

So there is this weird phenomenon that occurs when you follow these specific rules: If ODD 3x+1 If EVEN x/2 The theory is that if you take a number through these rules as far as possible you will achieve a never ending cycle of 4,2,1. So say for instance you start with 5 follow the ODD function to get 16 then even function for 8 again for 4 again for 2 again for 1 then 4, 2, 1, 4, 2, 1... As far as I am aware this has not been proven to work for every number and it is unsure if there could be other sequences like this that appear from numbers untried. I guess my point is for a discussion to see if it can't be proven.

This is the problems on the 46th International Mathematical Olympiad. My friends got excellent result from it, some of them are still very young, the youngest is 2 years smaller than me. That could depress me much. [as I even could not get the qualification to join the competition] http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/1dayenglish.pdf http://gifted.hkedcity.net/Gifted/ActReview/imo2005Mexico/pdf/2dayenglish.pdf