The Perfect Way to Multiply -Math Technique

[Stryder50]

Mathematicians Discover the Perfect Way to Multiply​

By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.​

EXCERPTS:
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For millennia it was widely assumed that there was no faster way to multiply. Then in 1960, the 23-year-old Russian mathematician Anatoly Karatsuba took a seminar led by Andrey Kolmogorov, one of the great mathematicians of the 20th century. Kolmogorov asserted that there was no general procedure for doing multiplication that required fewer than n2 steps. Karatsuba thought there was — and after a week of searching, he found it.

Karatsuba’s method involves breaking up the digits of a number and recombining them in a novel way that allows you to substitute a small number of additions and subtractions for a large number of multiplications. The method saves time because addition takes only 2n steps, as opposed to n2 steps.

Credit: Lucy Reading-Ikkanda / Quanta Magazine.
“With addition, you do it a year earlier in school because it’s much easier, you can do it in linear time, almost as fast as reading the numbers from right to left,” said Martin Fürer, a mathematician at Pennsylvania State University who in 2007 created what was at the time the fastest multiplication algorithm.

When dealing with large numbers, you can repeat the Karatsuba procedure, splitting the original number into almost as many parts as it has digits. And with each splitting, you replace multiplications that require many steps to compute with additions and subtractions that require far fewer.
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Mathematicians Discover the Perfect Way to Multiply

By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.

getpocket.com

 

[1srelluc]

I suck at math.....I pondered about getting a milling machine for my gun projects but (sigh) the old MK-I eyeball ain't what it used to be.

 

[The Irish Ram]

 

[Stryder50]

Being the current thread focused on math, seems I forgot this yesterday;

How Much Pi Do You Really Need?​

To celebrate Pi Day, we look at applications—from NASA to cars—that prove you can have too much of a good thing.
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Today is Pi Day, so named because the first three digits of pi are 3.14 and the date is March 14—or 3/14 in the format used in the United States. Yes, on most other parts of Earth today is also March 14, but they write that as 14/3—for them, the best Pi Day is July 22, (or 22/7) which is a fairly nice fractional representation of pi.

You can't actually write down all of pi since it's an irrational number and it has digits that go on forever. You can either use a fraction or write it as a decimal—like 3.14. But that's only three digits. How about 3.14159 or 3.14159265359 or even a trillion digits—wouldn't that be better? How many do you really need?

What Is Pi?
Let’s start with defining pi, also written as π. The most basic definition is that it’s the ratio of the circumference and the diameter of a circle. That means that if you take a circle and measure the distance across it (the diameter, d) and the distance around it (the circumference, C), then C/d = π. It doesn't matter what circle you use—this ratio is the same for all circles. A period at the end of a sentence has the same C/d ratio as the Earth's equator. (You can verify this yourself.)
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How Much Pi Do You Really Need?

To celebrate Pi Day, we look at applications—from NASA to cars—that prove you can have too much of a good thing.

www.wired.com