It's interesting that the 'exponent slide rule' did not use identical scales! This can be seen by the commutative property of multiplication:
In general: x*y = y*x
For exponentiation, the property vanishes and in general, y^x != x^y
The consequence of this, is that we require two different 'stretchings' for each axis. In stretching the axis of the multiplication table, the stretching was identical on each axis, a symmetry highlighted by the colorful line y = x at 2:08.
It could have one slider labeled 'exponent', which will have increments marked 'x' at distances proportional to ln x. The other slider could be labeled 'base' and will have increments marked 'b' at distances proportional to ln( ln b ) like the other. To exponentiate: we would line up any base with the '1' along the 'exponent' slide. Then we would look along the exponent rule until our desired exponent is found, and see the corrosponding result on the 'base' rule again!
Very cool of you to take the time and show people all about these lost wonders of calculation. I have a desk drawer full of them and love using them still today.
Though, did not understand just this one thing... from time 2:05 to 2:09 (the consolidation of points to a single line [that looked like y=x to me]. Now, my question is: why did you cover this point at all? I thought, the only thing we were interested in here was the stretching of the x and y axes... so as to stretch the f(x) = a / x curves (shown in various colors) to straight lines... to build the basis for the slide rule computation.
Would you mind explaining? Many thanks in advance.
Hey Nate, the Math Guy! You *completely* blew me over with your presentation (= explanation + animation) ! I understood the log concept but did not this aspect of it. Thank you so much!
Dont make me take out my slide ruler. EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
I'm starting out in Mathematics, I'm on Arithmetic right now. Lawrence Spector is a very good teacher. I wanna learn how to use the sliderule to carry on my pocket.
How about Ln(scale). To reach some decent separation between integers lets mutiply by a constant. MaxLen= K*Ln(10). To find a decimal position in scale is more or less easy. Logaritms transforms multiplications in adds. Is that corect?
You're the only person who explained how the slide rule works! I'm getting one, although I have no real use yet. Our science told us what Log, sin, tan, etc., which all has to do with the slide rule...
Hi, this was really cool! I am a sliderule user and collector. I use the sliderule every day, and like to see how accurate I can get my answers compared to what the calculator gives. I've gotten pretty accurate over the years. You have a nice presentation.
For any of you mathematicians out there who may be watching, here's an even more advanced question: What properties must a function of two variables satisfy in order for it to be possible to encode the function on two sliding scales?
Dr. Osborne!
relaXUE 1 month ago 10
@relaXUE Telelearn?
pkthunder9874 1 month ago
@pkthunder9874 haha yes. and im stuck lol
relaXUE 1 month ago 2
So what function does satisfy f(12/x)?
777rmb 1 month ago
Nice video. I'll probably stick with my Versalog 2 though - it's easier to take into an exam hall.
ralph17p 7 months ago
Oh man I wasted 30 seconds of my life and for what. I wanted to see what Y=12/X was :I
blajsad 7 months ago
It's interesting that the 'exponent slide rule' did not use identical scales! This can be seen by the commutative property of multiplication:
In general: x*y = y*x
For exponentiation, the property vanishes and in general, y^x != x^y
The consequence of this, is that we require two different 'stretchings' for each axis. In stretching the axis of the multiplication table, the stretching was identical on each axis, a symmetry highlighted by the colorful line y = x at 2:08.
Great vid!
Pkilcullen 9 months ago
It could have one slider labeled 'exponent', which will have increments marked 'x' at distances proportional to ln x. The other slider could be labeled 'base' and will have increments marked 'b' at distances proportional to ln( ln b ) like the other. To exponentiate: we would line up any base with the '1' along the 'exponent' slide. Then we would look along the exponent rule until our desired exponent is found, and see the corrosponding result on the 'base' rule again!
Pkilcullen 9 months ago
Great video on Logarithms! It's cool how you related multiplication tables to the idea of logs!
Here's my solution to the 'exponentiation slide rule':
Clearly, if: y = b^x
then ln y = x*ln b
we apply the natural logarithm again to get: ln( ln y ) = ln x + ln( ln b )
thus: ln( b^x ) = ln x + ln( ln b ) This expression lets us build an exponentiation slide rule!
Pkilcullen 9 months ago
I've gotta learn how to use these. It's something I always wanted to do, but haven't done.
Chewytube1 11 months ago
Parralel slides for exponetials
idwtsasoj 1 year ago
Very cool of you to take the time and show people all about these lost wonders of calculation. I have a desk drawer full of them and love using them still today.
CropDusterMan 2 years ago
log(a) + log(b) = log(ab)
Giblinono 2 years ago
That's a great video, but I noticed a little mistake: iso- isn't Latin, it's Greek ;)
arkelanfall 2 years ago
Though, did not understand just this one thing... from time 2:05 to 2:09 (the consolidation of points to a single line [that looked like y=x to me]. Now, my question is: why did you cover this point at all? I thought, the only thing we were interested in here was the stretching of the x and y axes... so as to stretch the f(x) = a / x curves (shown in various colors) to straight lines... to build the basis for the slide rule computation.
Would you mind explaining? Many thanks in advance.
somedeveloper 2 years ago
Hey Nate, the Math Guy! You *completely* blew me over with your presentation (= explanation + animation) ! I understood the log concept but did not this aspect of it. Thank you so much!
somedeveloper 2 years ago
Dont make me take out my slide ruler. EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
suterusu123 2 years ago
wow great! I loved the in depth explanation!
IncludeAustin 2 years ago
I'm starting out in Mathematics, I'm on Arithmetic right now. Lawrence Spector is a very good teacher. I wanna learn how to use the sliderule to carry on my pocket.
DokkenHolden 3 years ago
all your base are belong to us!
macsucks45 3 years ago
this video could be much shorter.
flytape8490 3 years ago
awesome demonstration!!
tpingt 3 years ago
it log or 10^x
jedimastert0810 4 years ago
How about Ln(scale). To reach some decent separation between integers lets mutiply by a constant. MaxLen= K*Ln(10). To find a decimal position in scale is more or less easy. Logaritms transforms multiplications in adds. Is that corect?
guillecrawley 4 years ago
Yes. That's it exactly.
TheMathGuy 3 years ago
You're the only person who explained how the slide rule works! I'm getting one, although I have no real use yet. Our science told us what Log, sin, tan, etc., which all has to do with the slide rule...
-Fave-
BuizelBlitz 4 years ago
Hi, this was really cool! I am a sliderule user and collector. I use the sliderule every day, and like to see how accurate I can get my answers compared to what the calculator gives. I've gotten pretty accurate over the years. You have a nice presentation.
sliderulex 4 years ago
Great video for those who care and have or can use a slide rule. I wear a Breitling B-2 slide rule watch.
InfinitelyManic 4 years ago
LOL...
BuizelBlitz 4 years ago
Mmm carino. La parte finale non è proprio chiarissima in quanto c'è una sola dimostrazione però rende l'idea.
La musica finale invece è ... orribile.
Nel complesso non male.
Evviva la Matematica!!
Tonty53 4 years ago
For any of you mathematicians out there who may be watching, here's an even more advanced question: What properties must a function of two variables satisfy in order for it to be possible to encode the function on two sliding scales?
TheMathGuy 4 years ago
All of your base are belong to us.
jedi1josh 4 years ago
Right on... I'm so glad I found this!
RobnJake 5 years ago
If you're ever without a pocket calculator, now you have a convenient multiplication table stored on two distorted rulers.
TheMathGuy 4 years ago
give me a few minutes and I will PM you the answer. I aint doing the exponential because I don't have THAT much free time.
Russoft 5 years ago