Build Yourself a Slide Rule

Nate the Mathematics Guy: Episode 3: Build Yourself a Slide Rule. Nate the Mathematics Guy explains what a slide rule is and how you can build one of your very own!

To build the slide rule you will need to download and print the following image (at 300 dpi):
http://img511.imageshack.us/img511/7657/sliderulenn3.gif

Category:

Howto & Style

Tags:

• nate
• mathematics
• guy
• themathguy
• slide
• rule
• multiplication
• calculator
• build
• yourself

[guillecrawley]

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?

[TheMathGuy]

Yes. That's it exactly.

[TheMathGuy]

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?

[RobnJake]

Right on... I'm so glad I found this!

[TheMathGuy]

If you're ever without a pocket calculator, now you have a convenient multiplication table stored on two distorted rulers.

[relaXUE]

Dr. Osborne!

[relaXUE]

@pkthunder9874 haha yes. and im stuck lol

[pkthunder9874]

@relaXUE Telelearn?

[777rmb]

So what function does satisfy f(12/x)?

[ralph17p]

Nice video. I'll probably stick with my Versalog 2 though - it's easier to take into an exam hall.

[blajsad]

Oh man I wasted 30 seconds of my life and for what. I wanted to see what Y=12/X was :I

[Pkilcullen]

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]

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]

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!

[Chewytube1]

I've gotta learn how to use these. It's something I always wanted to do, but haven't done.