Pure Mathematics

richlevy · 08-16-2005, 07:47 PM

I don't know why it stuck with me, but I still remember the concept of imaginary numbers.

Given that a square root of number is two equal numbers that when multiplied result in that number, and that a negative times a negative is a positive then -

-4 and +4 are both the square root of 16.

4i is the square root of -16. Since a negative number cannot really have a square root, but since it might occur in a formula, the square root of a negative number is an imaginary number (which is why it is marked 'i'). It can't exist but it has to be able to exist. It's sort of like mathematical antimatter.

If you consider that negative numbers themselves are a little fictitious (try fitting negative four apples into a bag), than imaginary numbers are just the result of extending the unrealistic into the absurd.

tw · 08-16-2005, 08:03 PM

Imaginary numbers are routinely used in things I must understand. There exist so many other 'variations' of mathematics that involve symbols I am not confortable with and concepts that I have difficulty with (such as manifolds, fields, and topology). For me, it helps to have some real world examples since when reading pure math, I don't always read what they had intended. Without those examples, I cannot 'benchmark' myself against what I was suppose to learn. Without those examples, then these mathematical concepts assume I already understand the principles; therefore they lose me in the underlying concepts.

One form of mathematics I wish I better understood is Galois fields. But then that type of math was not even listed. Gauss accomplished so much that I am not sure which is and is not Gaussian mathematics.

BigV · 08-17-2005, 12:01 AM

Quote:

Originally Posted by tw

Imaginary numbers are routinely used in things I must understand. There exist so many other 'variations' of mathematics that involve symbols I am not confortable with and concepts that I have difficulty with (such as --snip--

imaginary numbers?

Like, um, Social Security? Manufacturer's Suggested Retail Price? EPA gas mileage estimates? Eight hours of sleep? "Big Ten Inch" (Ok, Aerosmith gets a pass :wink: )

Yeah, I don't really understand them either.

wolf · 08-17-2005, 12:33 AM

Quote:

Originally Posted by tw

Imaginary numbers are routinely used in things I must understand.

That explains a lot.

dar512 · 08-17-2005, 12:48 AM

That was a cheap shot, Wolf

-- but it didn't stop me from laughing.

08-16-2005, 07:47 PM	#1
richlevy King Of Wishful Thinking Join Date: Jan 2001 Location: Philadelphia Suburbs Posts: 6,669	I don't know why it stuck with me, but I still remember the concept of imaginary numbers. Given that a square root of number is two equal numbers that when multiplied result in that number, and that a negative times a negative is a positive then - -4 and +4 are both the square root of 16. 4i is the square root of -16. Since a negative number cannot really have a square root, but since it might occur in a formula, the square root of a negative number is an imaginary number (which is why it is marked 'i'). It can't exist but it has to be able to exist. It's sort of like mathematical antimatter. If you consider that negative numbers themselves are a little fictitious (try fitting negative four apples into a bag), than imaginary numbers are just the result of extending the unrealistic into the absurd. __________________ Exercise your rights and remember your obligations - VOTE! I have always believed that hope is that stubborn thing inside us that insists, despite all the evidence to the contrary, that something better awaits us so long as we have the courage to keep reaching, to keep working, to keep fighting. -- Barack Hussein Obama

08-17-2005, 12:48 AM	#5
dar512 dar512 is now Pete Zicato Join Date: May 2003 Location: Chicago suburb Posts: 4,968	That was a cheap shot, Wolf -- but it didn't stop me from laughing. __________________ "Against stupidity the gods themselves contend in vain." -- Friedrich Schiller

08-16-2005, 08:03 PM	#2
tw Read? I only know how to write. Join Date: Jan 2001 Posts: 11,933	Imaginary numbers are routinely used in things I must understand. There exist so many other 'variations' of mathematics that involve symbols I am not confortable with and concepts that I have difficulty with (such as manifolds, fields, and topology). For me, it helps to have some real world examples since when reading pure math, I don't always read what they had intended. Without those examples, I cannot 'benchmark' myself against what I was suppose to learn. Without those examples, then these mathematical concepts assume I already understand the principles; therefore they lose me in the underlying concepts. One form of mathematics I wish I better understood is Galois fields. But then that type of math was not even listed. Gauss accomplished so much that I am not sure which is and is not Gaussian mathematics.

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