Number theory - Is there an intuitionist (i.e., constructive) proof of the infinitude of primes? Math.ucr.edu/home/baez/Alex_Alaniz_Lie.pdf. 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 is so your third step also involves dividing by zero which isn’t allowed! And see what happens as x>0 gets small. So, since = 1, that means that High School Teacher: Showing that approaches 1 as the positive value x gets arbitrarily close to zero does not prove that.
Beyond Calculus. Www.numbersimulation.site88.net. Calculus. Math21b, Fall 2003, Linear Algebra and Differential Equations. Nerd Paradise : Calculating Base 10 Logarithms in Your Head. Calculating base 10 logarithms in your head on the fly is a lot easier than you may think.
It is simply a matter of memorization and a little estimation... First memorize all the single digit base 10 logs. Don't worry, it's not as painful as it sounds. I even made the chart for you: Remember this rule from high school? And what about this one, you remember it too? Good. Example #1: base 10 log of 400 That's the same thing as log(4*100) which equals log 4 + log 100. log of 4 you know from the table above.
Now you may ask, what if it isn't just a number with a bunch of 0's after it? Example #2: base 10 log of 35 Suppose you wanted to find the logarithm of 35. Our guess: 1.545 Calculator says: 1.544068... Now you can convince all your friends and teachers that you are autistic. Example #3: base 10 log of 290438572: This is fairly close to log(2.9 * 100000000) = log 2.9 + log 108. Heart Curve. There are a number of mathematical curves that produced heart shapes, some of which are illustrated above.
The first curve is a rotated cardioid (whose name means "heart-shaped") given by the polar equation The second is obtained by taking the cross section of the heart surface and relabeling the -coordinates as , giving the order-6 algebraic equation The third curve is given by the parametric equations where. Heart Curve. What is the Heart Curve?
If you speak about a heart, you rather mean the heart figure than the heart shaped curve. Drawn Heart Curves topMethod 1 Method 2 Method 3 Method 4 Method 5 Method 6 Calculated Heart Curves topIt is a challenge to find formulas which produce hearts. The formulas y=sqr(|x|)+sqrt(1-x²) /\ y=sqrt(|x|)-sqrt(1-x²) are even better. More curves Sources: (Picture 1) Book 8, Eugen Beutel (1901) (2) Buch 4, Aufgabe 8.5.5., (3) MathWorld (simplified formulas), (4) H.
From the desk of Torsten Sillke Threedimensional If you choose y=0 respectively x=0, you get the equation of the 2D heart above on the left. Source: Gabriel Taubin [for example MathWorld (URL below)] The graphs were made by the freeware program "winplot" (Version 23.05.2000, URL below). Winword Hearts topAnd how do artists design a heart? The heart appears as a well known figure in character sets of programs under MS Windows. [1203.3150] Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge. Infinity Computer Calculates Area Of Sierpinski Carpet Exactly. A Sierpinksi carpet is one of the more famous fractal objects in mathematics.
Creating one is an iterative procedure. Start with a square, divide it into nine equal squares and remove the central one. That leaves eight squares around a central square hole. In the next iteration, repeat this process with each of the eight remaining squares and so on (see above). One interesting problem is to find the area of a Sierpinski triangle. So the area of a Sierpinski carpet after n iterations is (8/9)^n. But what is the area of the carpet after an infinite number of iterations? Ordinary mathematics has no answer to this question because it lacks the tools for handling infinity. In this case, the area of the carpet tends to zero as the number of iterations tends to infinity so the area of a Sierpinski carpet is zero.
That leaves many mathematicians with a sour taste in their mouths. For the last few years, Sergeyev has been championing a new type of mathematics called infinity computing. Grossone. - StumbleUpon. Accuplacer Practice Quiz.