Problem 226

[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

[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.

[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."?

[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!

[stijn263]

(..) 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..

[ed_r]

Well hooray for diversity

[hk]

Would everybody be happy if we changed "where s is the sawtooth function" in "where s is a sawtooth function"

[ed_r]

Who's "everybody"? Two dissenters out of, how many, 50K? Let's move on …

[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.

[JohnMorris]

Mathworld appears to agree with the engineering definition:

http://mathworld.wolfram.com/TriangleWave.html

http://mathworld.wolfram.com/SawtoothWave.html

[ishkur]

A look at the wikipedia page for the Blancmange curve shows this:



Hope that helps clear any lingering doubts.

[ed_r]

There are no doubts about the definition. (Some) people just don't like the name "sawtooth function".

[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?

[ed_r]

Yes, of course we can do without. But I don't see the need to change it.

[hk]

Why not if it gives some people the wrong impression?

[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.

[ed_r]

Edited to remove reference to "sawtooth" function. Let's hear no more about it.

[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.

[Tommy137]

That's not right

[ImRe]

Thx. It helped a lot.