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Is finding the Riemann Sum of a curve just finding the midpoint rectangular approximation?
It could be. In addition to a Midpoint Rectangular Riemann Sum there is also a Left Rectangular Riemann Sum, a Right Rectangular Riemann Sum, and a Trapezoidal Riemann Sum. When you are asked to compute a Riemann Sum, you must choose from the above list depending on the specific question, your teacher's preferences, and/or your own preferences.
What is the Riemann hypothesis?
The Riemann Hypothesis was a conjecture(a "guess") made by Bernhard Riemann in his groundbreaking 1859 paper on Number Theory. The conjecture has remained unproven even today. It states the "The real part of the non trivial zeros of the Riemann Zeta function is 1/2"
What is the answer to the world hardest math problem?
The hardest math problems are those which remain unsolved. One example is the Riemann Hypothesis, which asks if the non trivial zeroes of the Rieman Zeta Function all have real part 1/2. The Riemann Zeta Function is the sum of a discrete infinite series of a complex variable s (1/ns from n=1 to infinity) where the real part of s is greater than 1. The solution to this problem has implications for the distribution of prime numbers, and is one of the famous "millenial" problems. It was proposed by Bernhard Riemann in 1859. By "complex variable" we don't mean a complicated variable, we simply mean a number of the form ai + b, where i2 = -1. As noted above, the real part of s (b) must be greater than 1, or the series does not converge and the sum would therefore not be finite. There are other problems in mathematics, some which might be harder, but this one is an interesting one and merits closer scrutiny.
What mathematicians helped to discover alternatives to euclidean geometry in the nineteenth century?
Nikolai Lobachevsky and Bernhard Riemann
How many integers between 300 and 500 have the sum of their digits equal to A?
There are 3 whose sum is 45 whose sum is 57 whose sum is 69 whose sum is 711 whose sum is 813 whose sum is 915 whose sum is 1017 whose sum is 1119 whose sum is 1219 whose sum is 1317 whose sum is 1415 whose sum is 1513 whose sum is 1611 whose sum is 179 whose sum is 187 whose sum is 195 whose sum is 203 whose sum is 211 whose sum is 22.
