Mental calculation: powers?

[RetoCH]

Hello to all

Just stumbled on this forum and being fascinated enough to register :-). On my reserarch about mental calculators, I found some words from the famous Rüdiger Gamm that suggest he is puzzling together higher powers using some lower ones (a few years ago, he had to do so, nowadays he knows them all by heart).

Has any one here an idea how to calculate a higher power withut using pascals triangle?

Looking forward to discuss this a bit, greetings from a little country (Switzerland)

Reto

[neuro]

Hello to all

Just stumbled on this forum and being fascinated enough to register :-). On my reserarch about mental calculators, I found some words from the famous Rüdiger Gamm that suggest he is puzzling together higher powers using some lower ones (a few years ago, he had to do so, nowadays he knows them all by heart).

Has any one here an idea how to calculate a higher power withut using pascals triangle?

Looking forward to discuss this a bit, greetings from a little country (Switzerland)

Reto

maybe this is completely out of topic, but if you are content with reasonable approximations, higer powers are easily computed, mentally, by learning the logarithms of 2 to 9 and playing with them.

When I first bought a house, I got rather fast in mentally computing mortgage approximations by deriving high powers using logs.

Obviously, this fails if you are interested in natural numbers and precise results.

[smokeybob]

Grüezi, wier gohtts? (I have a 60% chance of being right... if not, ça va?)

I haven't read all of the book, only parts here and there - but check this book out.
Secrets of Mental Math

What's the need for doing this, by the way? Are you studying mental calculations, or you just wanna be able to show off to girls on the street?

[RetoCH]

That`s nice- "guet danke"...

Well, I enjoy the art of mental calculation and showing off is not my motivation. It`s just impressive to know how high some mental calculators could go in the past, today Rüdiger Gamm using mnemonics goes even higher...

Trying to find a fifth power of a 2 digit number is not the peak but already hard enough, this is the reason to ask for some help, mainly if a higher number can be "puzzled together" using lower powers (as stated by Rüdiger Gamm some years ago).

[smokeybob]

Myself, I've always been as lazy as possible. There have only been a few things where I really get into it and go through all the sources, look up papers etc.

However on this, I can't see any good sources where people are doing research in it - because it's not that important for pushing the boundaries of math, per-say. I don't know if I can help much more.

[RetoCH]

Thanks for your inputs so far, I agree that powers are not very important for math questions but still fascinating for mental challenges.