Mathematics

Okay, this has confused me for a while now. Arctanh and arccotanh seem to be two different functions. Yet their derivatives are the same. What's more when I plot the two in WA, the plots overlap (at least the real parts). However, when I make WA solve the equation Re(arctanh(x)) = Re(arccotanh(x)), it gives me no real solutions, and a bunch of completely random complex solutions. So what's the deal?

When we try to write Pi in decimal notation, we get an endless stream of digits. 3.141592653589723.....and so on forever. This seems counter-intuitive. You'd think that a simple thing, like the ratio between the radius and circumference of a circle, ought to be a simple, precise number. After all, isn't the Universe made almost entirely of circular and round things. Could the seeming lack of precision in Pi, be due to our human custom of using decimal notation. For example, if we divide something into 3 parts, each part is then, in decimal notation, an imprecise 0.333333333.... of the original. But suppose instead, we use Fractional notation. Then w…

I want to understand the logic behind Calculus, can you refer me to some material available online? I have done calculus before (about 2 years ago), and I'm looking for a book on the foundations of calculus, not a book on practical calculus. Also, what terms should I search for in search engines? If you would like to talk a bit about the foundations of calculus, that would be really appreciated.

Are there formalized statements about the fact that representation inflates the amount of information present? I mean in electronics a binary decoder is an example of how representation causes inflation, but I'm looking for more general statements about this before I feel it is necessary to make my own; order of preference here.

Im planning to solve the following problem with trial and error in c++ after solving this equation by calculating the partial derivatives and force them to be equal to ZERO we obtain the attached equations for a b c. as you can see we have to use the trial and error method to solve this problem for a b c the problem is the first guess of a b c. based on the first guess the answer changes and usually goes to infinity !!! Im asking you to help me to find the proper first guess. Ive attached a set of sample xi yi data to the post too. data_file.txt just in case I attach the c++ class I have programmed to this post too. Po…

Here is a cool trick to square numbers made up of repeating 1 (one). Count the number of repeating 1 in the number to be squared and put the digits ascending from 1 up to that number. That is, if there are four 1's in the number to be squared, put 1234. Then, put down the same numbers inversely, that is, 321. That’s it. It is so easy, it’s just mental math. Easy and fast. Let’s illustrate with an Example: If the number to be squared is 111 There are 3 repeating 1's. So, put down 123. Then, put 21 after 123. So, 1112 = 12321 See the pattern? Let's see another one, Square of 11111 =? There are 5 repeating 1's. So, put 12345. Then, put 4321…

Hi in my previous topic we reached to a conclusion that I need to find the minimum value of the following function . [math] cost(a, b, c) = \Sigma_i (y_i - a x_i^b - c)^2 [/math] "yi" and "xi" are the result of a complicated analysis on my lab data and I need to find a,b,c in a way that COST(a,b,c) function be minimum. I know its simple to use mathematical softwares like matlab or mathematica. but I have to develop my program with c++ so I need to know the algorithm of this process. can you help me with that ? I would be appreciated

First of all, pick the number of days a week that you would like to eat out. Multiply this number by 2. Add 5. Multiply it by 50. If you have already had your birthday this year . . . add 1762 If you have NOT had your birthday yet this year . . . add 1761 Subtract the four digit year that you were born. You should now have a three digit number: The first digit of this was your original number (i.e. how many times you want to go out to eat each week). The second two digits are your age!!! You can also amaze your friends or family members by asking them to pick a number between 1 and 10 and then follow the whole process. 2012 is the…

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.

Okay, I just woke up and have had only one cup of coffee so far this morning, so I'm not quite awake yet. When I'm in this sleepy-time condition I tend to wander aimlessly through the internet. This morning I found myself looking at a youtube clip claiming that 0+0=1. And all of the comments on that page were having a grand old time bashing the poster of this clip. (I clicked out of youtube and now I can't find the clip again.) Anyway, while having my first smoke outside, my mind began to wonder how and why 0+0=1 could come even close to being a true statement. What I came up with is probably laughable, but could you kind people of a higher intelligence than mine (an…

If you multiply two five digit numbers you can get the answer 123456789. Can you guess the two five digit numbers? This is a very beautiful puzzle and you might think that a big mathematical theory should be hidden behind it. But in fact its beauty is only incidental. Give it a try ... . . . Here is the Hint to help you solve the puzzle, 'Decompose the number (123456789) into its prime factors'. 123456789 = 3 x 3 x 3607 x 3803 Got it? OK, check it with the solution … scroll down . . . . . Find the solution url removed

prove that : [math]x=x[/math]

If a number can be expressed as a product of two whole numbers, then the whole numbers are called factors of that number. In other words, A factor is a whole number which divides exactly into a whole number, leaving no remainder. For example, 13 is a factor of 52 because 13 divides exactly into 52 (52 ÷ 13 = 4 leaving no remainder). 52 = 1 x 52 = 2 x 26 = 4 x 13 So, the complete list of factors of 52 is: 1, 2, 4, 13, 26, and 52 (all these divide exactly into 52). The simple technique to find the number of factors of a given number is to express the number as a product of powers of prime numbers or prime factors. To illustrate let's find the numbers…

Ask a friend to secretly write down ANY number (at least four digits long). e.g. 78341 Ask the friend to add up the digits... e.g. 7+8+3+4+1 = 23 ... and then subtract the answer from the first number. e.g. 78341 - 23 = 78318 Your friend then crosses out ONE digit from the answer. (It can be any digit except a zero) e.g. 7x318 Your friend then reads out what digits are left .e.g. 7-3-1-8 Even though you haven't seen any numbers, you can say what the missing digit is! EIGHT THE SECRET This great trick relies on the power of 9. How? Link removed by Moderator

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

. "button error" hey guys. as we know that [math]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/math] where the discriminant is [math] {b^2 - 4ac} [/math] and I thought discriminant is taken from the quadratic formula, which squaroot the result of discrimination. So, that's mean when discriminant's result is negative, the answer is not available. Yet, I want to explore more about the 'un-available root', I use calculator to calculate the equation that its discriminant is negative. Then, it bugging my mind somehow the x is founded! [math] x^2 - 3x + 4 = 0 [/math] [math] D = -7 < 0 [/math] [math] x = 1.5. [/math] did I miss anything here?

Here is a cool trick to add hours and minutes together: Let's try adding 3 hr 23 minutes and 2 hr 46 minutes together. Make the 3 hr 23 minutes into one number, which will give us 323 and do the same for the other number, 2 hours 46 minutes, giving us 246. Now add these two numbers together: 323 246 569 So, we have a total of 569. Now, if the last 2 digit is equal to or greater than 60, just add 40 to the total, otherwise keep it as it is. 569 + 40 = 609 And now, split the number to get the answer which is 6 hrs and 09 minutes!

I'm trying to solve a very simple logic problem. We've been asked to construct a truth table and then a Karnaugh map based on the truth table to simplify the expression, then create a 2nd truth table to verify that the simplified version (from the K Map) is logically equivalent. For some reason my two truth tables are not lining up so I must be doing something wrong. The question says that the variables X Y Z each represent sensors, the state of M is true (=1) when one or more sensors are on. For a truth table this would be every row aside from the first one where all are equal to 0, correct? Then my K Map gives me a group of 6 and a group of 2 which overlap…

Can someone please identify this equation and tell me what it's used for? (1-a)S(pi)(r^2)=4(pi)(r^2)2εδ(T^4)

You likely know the technique of multiplying any number by 11. Here is the trick to multiply a 2-digit and 3-digit number by 111. Multiplying a 2-digit number by 111 Example: 111 × 58 1. Write down the ones digit. > 8 2. Add the tens and ones; carry, if any. > 38 (5 + 8 = 13) 3. Repeat the previous step (and add carry, if any) > 438 (5 + 8 + 1 = 14) 4. Write the tens digit (add carry, if any) > 6438 (5 + 1 = 6) So, 111 × 58 = 6,438 Multiplying a 3-digit number by 111 Use right-to-left "sweeps" of 1, 2, 3, 2, and 1 digit. Example: 111 × 234 1. Write down t…

The Fibonacci numbers are a series of whole numbers in which each number is the sum of the two preceding numbers. Beginning with 0 and 1, the sequence of Fibonacci numbers would be 0,1,1, 2, 3, 5, 8, 13, 21 etc. The Fibonacci Number Tricks amazes almost everyone. For more click here Fibonacci Addition Trick Step 1: Choose two numbers Step 2: Form a Fibonacci sequence for ten numbers Example, Let us choose number 5 for the first number and 6 for the second number. Then add the numbers to get a Fibonacci sequence. 5+6 gives the 3rd number which is 11; 6+11 gives the 4th number which is 17. The entire sequence is as follows: 1st - 5 2nd - 6 3rd - 11 …

These are the famous people from past century sciences that have used numerology to dispher pi ratio. If this is so, then can numerology also be applied to facts in the science world???? Diophantus of Alexandria, 22/7 = 3.14285714285714 http://en.wikipedia...._exceeds_%CF%80 Isaac Newton 223/71 = 3.14084507042254 http://www.ms.uky.ed...h330/Newton.pdf MY PERSONAL FIND: This is my finding not using numerology of which HAS BEEN copyrighted and been validated. -10.86902388503848+14.01061653862827 = 3.14159265358979323846264338327950288419716939937510... I would like to know other's inputs on Issa…

So I've been trying to prep for an upcoming math competition by going through some problems. This one has me a little stuck, "Suppose [latex]f[/latex] is a differentiable function function on [0, 2] then there exists a point [latex]c\in [/latex] such that: [latex]f''©=f(0)-2f(1)+f(2).[/latex]" I am not sure this statement is true under these conditions, and think twice differentiable is probably required. Assuming that [latex]f[/latex] is twice differentiable I have tried applying the mean value theorem, and have been able to show that there exists [latex]a,b\in [0,2][/latex] and [latex]c\in [f'(a), f'(b)] [/latex] such that: [latex]f(0)-2f(1)+f(2)=f'(a)+f'(b)=f''©.…

Hello, just checking that this is right before I put it in my extension work. Is this the correct formula to find the velocity of an object falling without counting air resistance? mgh = 1/2 m^2 divide both sides by m gh = 1/2 v^2 v = sq (2gh)

These days we have become so much dependent on the mechanical devices that we have almost forgotten how to use our mind. We need calculators (if not computers) to add our shopping bills. Daily life tosses plenty of math problems our way. Of course, normal calculation can get boring. Here's the secret: Tricks & Shortcuts. Mental calculation comprises arithmetical calculations using only the human brain, with no help from calculators, computers, or even pen and paper.