How To Be A Smartass, Part 2

[Frawg]

Not something as fundamental as that for a relatively simple question. I mean, how would one forget the value of √2 when studying mathematics for a long time?

 

Remembering the decimal value of any irrational number is pointless beyond working though highschool algebra and precal (and nerd competitions)--it'd be like remembering the value of pi or e. Sure, remembering the decimal to one or two places to be able to understand where it is, but it's really best to preserve the value in its representative form (or fractional for rationals); first step is never really expanding pi into 3.141... (I approximate e to 2.7, pi to 3.14, and 2^(1/2) to 1.4). It keeps things clean and simple. I got through my Calc 1 course without ever really needing to use a calculator (or expand non-integers into decimal form) beyond error-checking and mindless (and often needless; '17+13') addition.

 

Properties and things that can be done with irrational numbers, like how they are defined or an algorithm on how to compute their decimal value is a different story all together.

Edited October 26, 2015 by Frawg

[Guest]

O_O.............oh sh!t.....so many math in here

[Renegade343]

Remembering the decimal value of any irrational number is pointless beyond working though highschool algebra and precal (and nerd competitions)--it'd be like remembering the value of pi or e. Sure, remembering the decimal to one or two places to be able to understand where it is, but it's really best to preserve the value in its representative form (or fractional for rationals); first step is never really expanding pi into 3.141... (I approximate e to 2.7, pi to 3.14, and 2^(1/2) to 1.4). It keeps things clean and simple. I got through my Calc 1 course without ever really needing to use a calculator (or expand non-integers into decimal form) beyond error-checking and mindless (and often needless; '17+13') addition.

I am well aware of that, but that does not excuse not remembering (or worse, not willing to remember) some common irrational numbers up to two or three decimal places for better communication and consistency, such as scientific reports. Yes, I am also well aware that it is a general convention to use π and e instead of their decimal forms, but I also know very little reports that employ liberal use of square roots to display results. 

 

That would be similar to not remembering what the value of acceleration due to gravity is when studying mechanics: You deal with them very commonly, so why not just remember them up to a few decimal points just to check things are alright, or to simply do measurements on the fly when needed?

[TheKingOfAllNoobs]

Not something as fundamental as that for a relatively simple question. I mean, how would one forget the value of √2 when studying mathematics for a long time?

Isn't the square root of 2 like, irrational?

 

Sorry for my ignorance

[Renegade343]

Isn't the square root of 2 like, irrational?

 

Sorry for my ignorance

Yes, but I would presume that for someone to study math for a long time, he/she should be able to memorise the decimal value of √2, at least up to two or three decimal points. 

[(XBOX)MK Ultra K11]

Not something as fundamental as that for a relatively simple question. I mean, how would one forget the value of √2 when studying mathematics for a long time?

Get drunk the same mistake making stuff happpens but on a much larger and worse scale.

[TheKingOfAllNoobs]

Yes, but I would presume that for someone to study math for a long time, he/she should be able to memorise the decimal value of √2, at least up to two or three decimal points. 

 

That's true.

 

Heck, my friend can recite pi up to 150 decimal places.

[Frawg]

I am well aware of that, but that does not excuse not remembering (or worse, not willing to remember) some common irrational numbers up to two or three decimal places for better communication and consistency, such as scientific reports. Yes, I am also well aware that it is a general convention to use π and e instead of their decimal forms, but I also know very little reports that employ liberal use of square roots to display results. 

 

That would be similar to not remembering what the value of acceleration due to gravity is when studying mechanics: You deal with them very commonly, so why not just remember them up to a few decimal points just to check things are alright, or to simply do measurements on the fly when needed?

 

When to use a decimal versus a symbolic representation is completely situational--it would be awkward to the perfect precision of a symbol in final results of applied sciences reports, and it would be awkward to not use the symbolic form in mathematical proofs that shows how you got that final result. And even then, declaring approximate values of popular irrational numbers (really, non-integers in general) depends on who the report is written for.

 

That said, when working though maths courses, I find it simpler, easier and frankly more educational if I try to avoid using decimal notation where possible (like my discrete math professor said, viewing the golden ratio as merely '1.618033988...' would be missing the point of the number). But that's just me. (And besides, like all other use-or-lose pieces of information, I can't retain a memory of a sequence of digits for S#&$)

 

It ultimately depends on who and where you are, what you're doing and what your audience is.

[unknow99]

That would be 2.718, to three decimal points. I did do a quick check on the other Euler constant, since it is the other Euler constant that is less than one. 

Yeeeeahh 2,718... e > 2^1/2 , sorry!

 

 

I bet you can't tell me Avogadro's constant without checking it.

Prrrt, give him something harder to guess than this, a mol is one of the basis of chemistry... ;)

[Renegade343]

When to use a decimal versus a symbolic representation is completely situational--it would be awkward to the perfect precision of a symbol in final results of applied sciences reports, and it would be awkward to not use the symbolic form in mathematical proofs that shows how you got that final result. And even then, declaring approximate values of popular irrational numbers (really, non-integers in general) depends on who the report is written for.

That is partially why I said the memorisation of some common irrational functions should be done. 

 

That said, when working though maths courses, I find it simpler, easier and frankly more educational if I try to avoid using decimal notation where possible (like my discrete math professor said, viewing the golden ratio as merely '1.618033988...' would be missing the point of the number). But that's just me. (And besides, like all other use-or-lose pieces of information, I can't retain a memory of a sequence of digits for S#&$)

I use it to conduct operations in my head for quick checks. I know the exact formula, but sufficient decimal representations provide faster mental computation overall. All I am saying is remembering common irrational numbers to at least two or three decimal places should be done if doing math all the time; any more depends on preference.

[(XBOX)MK Ultra K11]

1. Attend another mathematics class for the course (Basic Calculus). 

2. Calculus professor does mathematics with a √2 value in the mix, gets the result wrong due to using the wrong value of √2. 

3. Someone points it out, professor starts to try and find the correct value for √2. 

4. I get frustrated. 

5. I stood up, got to the board, and found the value for √2 with Taylor expansion, using less time and less space than the professor did. 

6. Professor was in shock as I exit the class early. 

 

Another true story.

No absolutely wrong. You change yourself into a donkey with an IQ of 700.