John Curl's Blowtorch preamplifier part II

[billshurv]

And for that we have people much cleverer than me. I am glad they exist. But I am not in their league and happy to accept that. Hey even Einstein needed help with his geometry, and I guess you were referencing Riemannian geometry when you mentioned 'maths for the sake of maths'.

 

[Markw4]

What primarily makes math different from other areas of human knowledge, is it that the right answer to a question is a matter of fact and not opinion?

 

[Bonsai]

Stanford mathematician, Keith Devlin wrote - "The most beautiful equation"

e (raised to the i*pi) +1 = 0

Why is Euler's formula so breath-taking? And what does it even mean?


thx-RNMarsh

'

Its more interesting if you write

e (raised to the i*pi) = -1

 

[billshurv]

no, because 0 is very important concept in mathematics. You can't lose that! After all Romans had no concept of zero and look where it got them.

 

[billshurv]

What primarily makes math different from other areas of human knowledge, is it that the right answer to a question is a matter of fact and not opinion?

So what about all the conjectures in mathematics?

 

[Markw4]

Math is about deductive reasoning starting from a given set a axioms. That's what makes it possible to have answers as fact and not as opinion.

But, most or all of what we actually know and can know about the world and reality is necessarily inductive.

 

[DPH]

Mathematics is critically important because otherwise we engineers wouldn't have anyone else to make fun of for being a goofier lot.

And e^(iπ)+1=0 is definitely the best form of the equation. It's a spectacular piece of glue to translate disparate equations.

 

[billshurv]

Glue! I understand glue. It sticks me to other things

 

[Markw4]

Interesting conjectures are ones for which inductive evidence exists, but deductive proof is missing, IMHO.

 

[Waly]

Interesting conjectures are ones for which inductive evidence exists, but deductive proof is missing, IMHO.

WTF are you talking about? Induction evidence is proof since Peano and Dedekind. There were attempts to build a constructive mathematics, without induction, and the Zermelo axiom, some time at the beginning of the 20th century, and after some 50 years of efforts they have successfully rewritten arithmetic to the point they were able to "constructively" add two arbitrary integers, otherwise said, "constructively" prove that 1+1=2. Nice try.

 

[Markw4]

The Problem of Induction (Stanford Encyclopedia of Philosophy)

 

[Waly]

The Problem of Induction (Stanford Encyclopedia of Philosophy)

Yes, Philosophy, not Mathematics (in despite of the appearance). No conclusions in the paper too, the question arising right away is "so what"?

 

[Mark Johnson]

First mouser.com , now digikey.com : BF862 NJFET EOL

Might buy a few hundred more just to be on the safe side

 

[31697B]

I am certain the brighter ones here can solve at least one of these problems.......

List of unsolved problems in mathematics - Wikipedia


-RM

 

[scott wurcer]

Sometimes maths for the sake of maths later turn out to have practical application.

I was very proud of myself (not being a maths guy) when after reading years of bad approximations of the efficiency of class G and class H amplifiers I derived it in closed form as an appendix in an ISSCC paper. It became the textbook standard derivation.

I tried to instill a little admiration for the beauty of Euler's equation in my digital RIAA article, simple algebra to do complex phasors, design both analog and IIR filters with the same equations, etc.

 

[31697B]

What does your wall of reference say?

Its here..... 5 Math Equations That Change the Way You See the World



-RM

 

[31697B]

I was very proud of myself (not being a maths guy) when after reading years of bad approximations of the efficiency of class G and class H amplifiers I derived it in closed form as an appendix in an ISSCC paper. It became the textbook standard derivation.

I tried to instill a little admiration for the beauty of Euler's equation in my digital RIAA article, simple algebra to do complex phasors, design both analog and IIR filters with the same equations, etc.

Old memory playback.... why is their efficiency only quoted at max output? When at lower output power it is not always better than others?


-RM

 

[Destroyer OS]

It puts together, in one formula, calculus (the e number), geometry (the pi number), algebra (the i number) and arithmetic (the 1 number). Hence, this formula illustrates the unity of mathematics.

Holy smokes... Waly contributed something to the forum. Albiet minor, everyone throw a nickle into the hat so we can buy him a cookie.

I have to wonder if several other members of a more prime age would like to not spend their last years on a math problem. Now I might be able to get my uncle to solve one because he thinks about, gets up 4 hours later writes down the answer, and goes back to sleep for another 4 hours.

 

[martin clark]

And e^(iπ)+1=0 is definitely the best form of the equation. It's a spectacular piece of glue to translate disparate equations.

It also completely defines two transcendental numbers in terms of the unit - via a power relationship, of all things, involving a fundamentally-useful constant.

Euler's result is a sublime work of pure mathematics.

 

[DPH]

Holy smokes... Waly contributed something to the forum. Albiet minor, everyone throw a nickle into the hat so we can buy him a cookie.

I have to wonder if several other members of a more prime age would like to not spend their last years on a math problem. Now I might be able to get my uncle to solve one because he thinks about, gets up 4 hours later writes down the answer, and goes back to sleep for another 4 hours.

Math at its pinnacle has been a young man's (woman's!) sport. That is changing over time as problems being solved are becoming more team-based than individuals, but there's been quite a bit of ink spilled on that phenomenon.

And I agree, Martin; Euler's body of work is beyond sensational.