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Mathematicians

Often, to completely understand the importance of a mathematical theory, it's essential to know about the person who developed it. This category is where all questions about historically significant mathematicians should be asked.

6,570 Questions

What is the physical interpretation of bessel function?

spherical bessel function arise in the solution of spherical schrodinger wave equation. in solving the problem of quantum mechanics involving spherical symmetry, like spherical potential well, the solution that is the wave function is spherical bessel function

What is a value that represents the evening out of the values in a set of data?

It's the mean, to get the mean, add all of the numbers up together and divide however many numbers are there, and 0 counts as one of the numbers for that if you have it.

What does a vertical line tell you?

A vertical line can be used to test whether or not a graph is a function.

If you are fourteen and hes turning seventeen this year is that too old for a relationship?

nope , if you can do everything necessary to make a relationship to work then there is no reason why you shouldn't get into one.

What is the effect on the world today due to World War 2?

This question calls for an opinion, at least to some extent, but I will offer one: The abomination of World War 2, coupled with the development of nuclear weapons, has so far prevented World War 3 for over 60 years.

The first half of the 20th Century saw the two most destructive wars in all history, largely due to massive changes in technology enabling all sides to kill and maul one another in increasingly brutal and imaginative ways.

World War 1 wasn't even called that until World War 2 started. Before 1939, the First World War was simply called The Great War, or sometimes The War to End Wars. Many people thought that after the unmitigated horror of 40 million casualties on all sides, unimaginably terrible conditions in the trenches, that there could simply never be another war. (Death, in a way, was the least of a soldier's problems compared with what he felt, saw, smelled and heard around the clock for four godawful years.)

But they were wrong. Germany had lost a generation of young men in WW1, just as had France and Britain, yet Germany felt a thirst for revenge, especially on the French, that could only be quenched by throwing away another generation of young men. And even though Germany had a lower birth rate than France, in 1940 the French Army pretty much gave up without a fight and there stood Adolf Hitler astride most of Europe, striking at the Soviet Union and seriously threatening to take over the whole world!

Japan wanted to hold the power over all of Asia, so they struck at China in 1931 and eventually struck at us in 1941. I think it's fair to say that between them, Germany and Japan wanted to at least rule their respective halves of the world. Had they won, sooner or later they'd have been at each other's throats.

It took a lot of hard fighting and, frankly, a lot of luck to beat Hitler in Europe and the Japanese on the other side of the world. There were about 40 million casualties in WW1. It's estimated that WW2 cost between 50 and 60 million DEAD. That's not including the wounded, maimed and missing.

The Germans were only beaten when they were crushed between allied armies coming at them from east and west. They only quit after Hitler killed himself. The Japanese wouldn't quit until the U.S. dropped two atomic bombs on them. Up until then they'd been arming women and children with sharpened bamboo sticks to fight the Americans on the beaches!

After WW2 ended, the Soviets got The Bomb, too, and the Cold War started, so called because there wasn't nearly as much shooting as there had been in WW2. There was Korea, of course, and Vietnam, and the Wars of Partition in Palestine and India and a whole host of other little "brushfire" wars costing a few thousand lives here and there, but nothing on the scale of 60 million dead.

Yet.

It's been 62 years since the end of WW2. Do you think enough time has passed for us to have forgotten the lessons? We've had nuclear showdowns but never a nuclear war; do you know that there are people in high military places who speculate whether humans could survive one? The little brushfire wars continue to take a few thousand lives here and there, but what if a big wind comes up and whips up the flames and a little brushfire becomes a world wide forest fire? What then?

There have been good things that came out of the war. I think the space race was a good thing. It started with ballistic missiles to hurl explosives at each other, but evolved into human exploration, which comes naturally. There are always unintended consequences of all human endeavor, but in the long run I think it's good. Computers are good. They came in part out of the necessity to compute fall of shot in artillery duels; now we have the internet and I can write answers to questions (right or wrong - your choice). The internet fuels discussion and human interaction. It also provides a place for those who would spew hatred and malice. But I'm a believer in freedom of speech. I resist censorship, even of the malicious haters. They can be countered by free thinkers. The proof of the theory of Plate Tectonics came out of WW2 in the process of antisubmarine warfare. Israel came out of WW2 as a direct result of the Holocaust. I think both are good, although I wish Israel would make allowances for a Palestinian homeland. If the Jews deserve a homeland of their own, so do the Palestinians. Both have suffered endlessly.

But I do worry that, as we get farther and farther away from the horrors of a really big war that we could get into another one. We see in Iraq and Afghanistan what the troops suffer: Improvised explosive devices tearing off arms and legs ... explosively formed penetrators able to go through the depleted uranium armor of even an Abrams tank - and we watch it go on, helplessly, day after day, and no one seems to know how to stop it. What if a wind comes up ...?

Where was Ruth Russell Williams born and raised?

Ruth Russell Williams was born in Townsville, North Carolina. She was my grandmothers cousin so you know our family is very proud of her

What are the differences between the Emperical Rule and Chebyshev's Theorem?

The Empirical Rule applies solely to the NORMAL distribution, while Chebyshev's Theorem (Chebyshev's Inequality, Tchebysheff's Inequality, Bienaymé-Chebyshev Inequality) deals with ALL (well, rather, REAL-WORLD) distributions. The Empirical Rule is stronger than Chebyshev's Inequality, but applies to fewer cases.

The Empirical Rule:

- Applies to normal distributions.

- About 68% of the values lie within one standard deviation of the mean.

- About 95% of the values lie within two standard deviations of the mean.

- About 99.7% of the values lie within three standard deviations of the mean.

- For more precise values or values for another interval, use a normalcdf function on a calculator or integrate e^(-(x - mu)^2/(2*(sigma^2))) / (sigma*sqrt(2*pi)) along the desired interval (where mu is the population mean and sigma is the population standard deviation).

Chebyshev's Theorem/Inequality:

- Applies to all (real-world) distributions.

- No more than 1/(k^2) of the values are more than k standard deviations away from the mean. This yields the following in comparison to the Empirical Rule:

- No more than [all] of the values are more than 1 standard deviation away from the mean.

- No more than 1/4 of the values are more than 2 standard deviations away from the mean.

- No more than 1/9 of the values are more than 3 standard deviations away from the mean.

- This is weaker than the Empirical Rule for the case of the normal distribution, but can be applied to all (real-world) distributions. For example, for a normal distribution, Chebyshev's Inequality states that at most 1/4 of the values are beyond 2 standard deviations from the mean, which means that at least 75% are within 2 standard deviations of the mean. The Empirical Rule makes the much stronger statement that about 95% of the values are within 2 standard deviations of the mean. However, for a distribution that has significant skew or other attributes that do not match the normal distribution, one can use Chebyshev's Inequality, but not the Empirical Rule.

- Chebyshev's Inequality is a "fall-back" for distributions that cannot be modeled by approximations with more specific rules and provisions, such as the Empirical Rule.

What are the Eulers formulas for the Fourier coefficients?

I think the following Wikipedia link on Fourier Series (see related links below), has the information that you're looking for.

Where did charle Babbage live?

Charles Babbage lived w/ his parents in London,England