Mathematics

Johannes Kepler was the greatest mathematician ever. I found some quotes of his recently. http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Kepler.html From a 1605 letter My aim is to say that the machinery of the heavens is not like a divine animal but like a clock (and anyone who believes a clock has a soul gives the work the honour due to its maker) and that in it almost all the variety of motions is from one very simple magnetic force acting on bodies, as in the clock all motions are from a very simple weight. Letter to J. G. Herwart von Hohenburg, 16 February 1605, KGW 15, 146. From the introduction, written in 1618, to Book V of The Harmony…

Hello, I'm a junior in Highschool, currently taking Algebra II. The reason I'm making this topic, is due to the many problem's i often find myself facing, when trying to work out problem's. Previous to this class, I've taken two classes of basic Algebra and one course in basic geometry, and to this day, comprehend very little of it. At this point in time in the class, we are reviewing the algebra 1 material, and i am at a big loss. We had a practice test today, covering the materials so far, and out of 25, i missed at most 12. For the most part, the way to solve the problem's is what trip's me up, and i often spend loads's of time picking number's from my head, …

It is seemed that I found the simple proof of FLT in the binary system. Here it they be: Numbers D = (a+b)^n-(c-b)^n-(c-a)^n and E = a^n+b^n-c^n + D (or -D) have DIFFERENT parities. The parity of number D is a dual parity even number (from a, b, c). But the parity of number E has another value (with specific grouping of the members of sum). Detailed calculations will be published in proportion to their readiness.

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…

In geometrical constructions using compass alone, we should restrict ourselves to two fundamental constructions: To find the points of intersection of two circles. To draw a circle with given center and radius. Can anyone tell me how to find the middlepoint of a given arc using only a compass?

I've been thinking about this problem for a few months now, are irrational numbers feasable as Cryptographically Secure PseudoRandom Number Generators (CSPRNG). I know on their own the digits of an irrational number would do a terrible job of this, because of the predictability once anyone found what number was being used. I also know that irrational numbers become periodic when expressed as continued fractions. Also, calculating more than a few thousand digits of even a square root costs a lot of computer power. But what if you only use a few digits from a number of irrationals, and not the first few digits either, and then transposed those digits so that they …

Prove that for all positive x, y and z (x+y)^z + (y+z)^x + (z+x)^y > 2

Hi everyone, im new here but i need some help Ive been asked to find the angle between the gravity and gravitational vectors as a function of latitude where gravity is pointing to the center of the earth and the gravitational vector is the sum of the gravity vector and centripetal vector. Can anyone help? Thanks

hi, While solving a calculus problem today related to "cross sections" I derived a formula to calculate the area of an equilateral triangle. So I was just curious whether the formula I came up with is already in use or it's....? The formula: [math]A(s)=\frac{s}{2}\sqrt{s^2 - \frac{s^2}{4}}[/math] What do you guys think?

The title for this post is inappropriate sorry, I hit post when I should have hit preview. I'm trying to re-arrange the first equation in the series below to the format [math] y=a(x-p)^2+q [/math] Using the completing the square method, now I have a process down where I get the right answers. But I don't understand what happens to the "8x" them in the last step...I just leave it out and take the sqroot of the "16" and the "x^2" to get the (x-4) in brackets? I don't fully understand why one-half of the coefficien of the x-term is added and subtracted either? [math] F(x) = 3x^2-24x+40 [/math] [math] F(x) = 3(x^2-8x)+40 [/math] [math] F(x)…

why is y=-f(x) a reflection of the graph y=f(x) accross the x-axis?

This is from the book, need help changing it into mathematical model. "Consider a tank used for certain hydrodynamic experiments. After one experiment the tank contains 200 litres of a dye solution with a concentration of 1 g/litre. To prepare for the next experiment, the tank is rinsed with fresh water flowing in at a rate of 2 litres/min, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank readches 1% of its original value."

OK this has been annoying me, I'm sure it's relatively simple and I'm just missing something... like the power of thought... show that: [math] \sum_{l=0}^{n-1}(2l+1)=n^2 [/math]

How would you factor: A^3 + B^3 + A^2 - B^2

Basically, I've slept through most of my basic education, and now I'm lusting for some Maths. The problem at hand is this: in what sequence should I go through the subjects? I got CliffsQuickReview Basic Math and Pre-Algebra, and since I'm about to be done with it, I was wondering what should be next on my list: Algebra, Calculus, Trigonometry, etc. I would appreciate it if someone gave me a proper summary that spanned subjects and their sequences. How many Calculuses are there--as in Calculus 1, Calculus 2, etc? How many Algebras? etc. Thanks in advance.

Hi all, Have been having some problems with the following math problem I was given last week: A solid cube of mass M and side a has one corner at the origin and three sides along the positive x,y and z axes. The square of the distance of the mass element dM = pdV rom the z-axis is x^2 + y^2 so that the moment of inertia of the cube around the z-axis is given by I = integral (x^2 + y^2) pdV taken throughout the volume V of the cube. If the cube has constant density, prove that I= (2/3) Ma^2 Any help/tips would be most appreciated!

I cannot find a way to prove this: A function r(n), where n is a positive integer, gives the number n with its digits inverted. Prove that for positives integers a and b, the two numbers 4(a^2) + r(b) and 4(b^2) + r(a) cannot be simultaneously perfect squares. Can anyone help me?

I'm currently taking pre-calculus and I'm learning that, when there is a constant c, then the equation of c = xy is the equation for an inversely proportional relationship of x and y. This makes sense, because if x decreases, y has to increase to keep c at its current constant rate. However, is this really the only inverse proportionality equation? It seems to me that c = x + y would also be inversly proportional, since 7 = 2 + 5 as well as 7 = 6 + 1. Notice how when one goes up, the other goes down, which is really the only requirement for an inverse proportionality relationship. Am I right, or am I stoned?

Anyone know how to factor on a TI-83+?????????

When solving a system using augmented matricies, how do u know when if the solution is inconsistent, if you continuously are trying to get th identity matrix

Hi, I have read from somewhere that random numbers generated by computers are really pseudo-random numbers in reality. If this is true, could anyone tell me what kind of patterns exist in the random numbers generated by computers that make them pseudo-random numbers? thx.

Hello could you please explain me with easy words how do you find out the domain and range of a function, for example f(x) =(x+5)^3+2 how would you know the domain and range of that function? thank you

hello I'm asked to write the equation y= 2x^2-4x+6 in the form y= a(x-h)^2 this is what i have been doing first I divide by 2 x^2-2x+3 then I try to complete the square (x^2-2x+1)+3 (x+1)^2 now i don't know what else to do Should I multiply that one times 2 because I divided by two and then add it to 3 to get 5? and so the answer would be (x+1)^2+5 But I know that's wrong because I graphed both equations and they aren't the same graph please help me.

Could you find all positive integer solutions to ... x^y - y^x = x + y

The theory that I am attempting to formulate is being complicated by the intrusion of ancient Greeks into the mix. Their number system is decimal in nature (probably lacking zero). My question is this. How old would a decimal Greek number system be likely to be? Could it be older for instance than the Arabic Islamic system which, by definition, must be newer than 500AD I always believed that the Muslims invented the decimal system. A date would be useful. :-) :-) -------------------------------------