Page 1 of 2
Problem 226
Posted: Sat Jan 03, 2009 7:22 pm
by albert
Code: Select all
In Euler226 The definition of S(x) defines a function like
* *
* * *
* * *
* *
In electronics this is called a triangular wave form.
This is how a sawtooth is wave form looks like.
* *
* * * *
* * * *
* * *
This would define S(x) as the distance to the preceding integer.
I think this may be need of clarification.
Groetjes Albert
Re: Euler 226: sawtooth or triangular wave?
Posted: Sat Jan 03, 2009 8:03 pm
by quilan
Saw tooth can be defined as the distance x is to the closest integer. So it's a triangle wave.
Edit: I see what you're saying, as that's correct for Electronics / etc. Some clarification could probably be used.
Re: Euler 226: sawtooth or triangular wave?
Posted: Sat Jan 03, 2009 9:29 pm
by daniel.is.fischer
In real life, there are saws with differently shaped teeth, let's call them mathematically shaped and electronically shaped
In mathematics, the distance to the nearest integer is commonly called the saw-tooth function (or Weierstraß' saw-tooth function if one wants to be more precise). Electronics follows a different convention
So, how should we clarify it?
"Note (for electrical engineers): This saw-tooth function is not the one you're used to."?
Re: Euler 226: sawtooth or triangular wave?
Posted: Sat Jan 03, 2009 9:40 pm
by ed_r
Our definition goes back to at least
1937.
IMHO, proponents of such modern-day sorcery as ... "electronics" (
*ugh* 
) ... should just live with it.
And before you rush to complain: yes, as it happens, I
am typing this into an abacus!
Re: Euler 226: sawtooth or triangular wave?
Posted: Sun Jan 04, 2009 10:20 pm
by stijn263
daniel.is.fischer wrote:(..) In mathematics, the distance to the nearest integer is commonly called the saw-tooth function (or Weierstraß' saw-tooth function if one wants to be more precise). Electronics follows a different convention
Not just electronics, the saw-tooth function they teach in my
mathematics study is the one shown by
albert in the first post..
Re: Euler 226: sawtooth or triangular wave?
Posted: Mon Jan 05, 2009 7:29 pm
by ed_r
Well hooray for diversity
Re: Euler 226: sawtooth or triangular wave?
Posted: Mon Jan 05, 2009 7:46 pm
by hk
Would everybody be happy if we changed "where s is the sawtooth function" in "where s is a sawtooth function"
Re: Euler 226: sawtooth or triangular wave?
Posted: Mon Jan 05, 2009 8:58 pm
by ed_r
Who's "everybody"? Two dissenters out of, how many, 50K? Let's move on …
Re: Euler 226: sawtooth or triangular wave?
Posted: Tue Jan 06, 2009 12:13 am
by quilan
To be fair, I also thought it meant the jagged sawtooth wave until I realized the function would look nothing like it did in the picture. A quick trip to wiki land gave me the right idea for the curve.
Re: Euler 226: sawtooth or triangular wave?
Posted: Tue Jan 06, 2009 1:04 am
by JohnMorris
Re: Euler 226: sawtooth or triangular wave?
Posted: Tue Jan 06, 2009 1:49 am
by ishkur
A look at the wikipedia page for the Blancmange curve shows this:
Hope that helps clear any lingering doubts.
Re: Euler 226: sawtooth or triangular wave?
Posted: Wed Jan 07, 2009 7:16 am
by ed_r
There are no doubts about the definition. (Some) people just don't like the name "sawtooth function".
Re: Euler 226: sawtooth or triangular wave?
Posted: Thu Jan 08, 2009 8:34 pm
by hk
Anyhow. I f one looks up sawtooth one does not find the form we need.
Is the mentioning of "sawtooth function" really necessary? Cannot we do without?
Re: Euler 226: sawtooth or triangular wave?
Posted: Thu Jan 08, 2009 8:56 pm
by ed_r
Yes, of course we can do without. But I don't see the need to change it.
Re: Euler 226: sawtooth or triangular wave?
Posted: Thu Jan 08, 2009 9:24 pm
by hk
Why not if it gives some people the wrong impression?
Re: Euler 226: sawtooth or triangular wave?
Posted: Thu Jan 08, 2009 11:50 pm
by JohnMorris
How about changing "where s is the sawtooth function" to "where s has the form of a triangle wave".
The first three Google hits for "Triangle wave" (to Wikipedia, Mathworld and some audio site) all show pictures of the right thing.
Re: Euler 226: sawtooth or triangular wave?
Posted: Fri Jan 09, 2009 7:01 am
by ed_r
Edited to remove reference to "sawtooth" function. Let's hear no more about it.
Re: Problem 226
Posted: Thu Apr 23, 2009 4:51 pm
by ImRe
I'm sort of stuck on this one.
Can somebody verify if the area under the circle between the intersection points are
0.09040954?
Thx.
Re: Problem 226
Posted: Thu Apr 23, 2009 5:17 pm
by Tommy137
That's not right
Re: Problem 226
Posted: Fri Apr 24, 2009 1:00 pm
by ImRe
Thx. It helped a lot.