### How do I slide rules?

Posted:

**Sun Sep 29, 2013 11:31 am**I could look it up, but if anyone can explain it to me it'll be you guys ;D

Bringing Science to Life... then chatting about it

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Posted: **Sun Sep 29, 2013 11:31 am**

I could look it up, but if anyone can explain it to me it'll be you guys ;D

Posted: **Sun Sep 29, 2013 12:13 pm**

Andy's slide rule, or just slide rules in general?

Posted: **Sun Sep 29, 2013 12:58 pm**

Slide rules in general.

Posted: **Tue Oct 01, 2013 9:46 pm**

Ah, sure. The actual (iPhone) version has an automatic mode -- which I haven't quite perfected in this version yet.

There are a bunch of ways to use it... but the place to start is with multiplication. When the slide rule opens up, look for rows "D" and "C", right on top of each other. Now move the slider (aka my name for the middle slidey piece) so that the 1 on the C scale lines up with the 2 on the D scale. Now any number x on the C scale is directly above 2x on the D scale. So 2 is above 4, 3 is above 6, and so on.

So move the 1 on the C scale over y on the D scale... and under any number x, you'll see y*x on the D scale.

Magnitude is up to you to remember. Which is important when finding something like 2*6. The true answer, 12, is off the charts (above 10) you need to modify the steps a bit. Instead of lining up 1 on the C scale, line up 10 on the C scale with 2 on the D scale. (The 10 is labeled as 1, since slide rules kinda ignore magnitude) Then 6 will be just above 1.2. You just need your brain to remind you "hey, this isn't right, the decimal point needs to be shifted!"

And ta-da, you can now multiply with two (digital) plastic sticks!

There are a bunch of ways to use it... but the place to start is with multiplication. When the slide rule opens up, look for rows "D" and "C", right on top of each other. Now move the slider (aka my name for the middle slidey piece) so that the 1 on the C scale lines up with the 2 on the D scale. Now any number x on the C scale is directly above 2x on the D scale. So 2 is above 4, 3 is above 6, and so on.

So move the 1 on the C scale over y on the D scale... and under any number x, you'll see y*x on the D scale.

Magnitude is up to you to remember. Which is important when finding something like 2*6. The true answer, 12, is off the charts (above 10) you need to modify the steps a bit. Instead of lining up 1 on the C scale, line up 10 on the C scale with 2 on the D scale. (The 10 is labeled as 1, since slide rules kinda ignore magnitude) Then 6 will be just above 1.2. You just need your brain to remind you "hey, this isn't right, the decimal point needs to be shifted!"

And ta-da, you can now multiply with two (digital) plastic sticks!

Posted: **Wed Oct 02, 2013 4:31 pm**

A great way to figure out how slide rules work is to make a simple paper slide rule. Then you can actually see things like how 1 to 2 is the same distance as 2 to 4 and 4 to 8.

I made one a long time ago, don't know where it is

I made one a long time ago, don't know where it is

Posted: **Fri Oct 04, 2013 8:35 am**

Thanks, this helped a bunch!A Random Player wrote:A great way to figure out how slide rules work is to make a simple paper slide rule. Then you can actually see things like how 1 to 2 is the same distance as 2 to 4 and 4 to 8.

I made one a long time ago, don't know where it is

I was bored in class (don't judge me!) and I decided to go ahead and try at making a slide rule. However, I was stuck on multiplication! Then during recess I took a quick trip to the school library and did some research, and rediscovered the log(ab) = log(a) + log(b) rule. From that I made a slight design, which, however, looked nothing like the true slide rules. (started doing more in depth research soon as I got home) Anyway, next time I'm bored in class Ill try to make a better design, as this is quite interesting.

Posted: **Mon Oct 07, 2013 8:39 am**

Alright, I made a better prototype. However, a calculator and paper aren't what you'd call accurate when it comes to placing the numbers in the right spot.

Anyway, while working on this I found out a few neat properties of logarithms!

For instance, log a / log b = log base b of a. I have no axiomatic proof of this (yet) but it appears to work fine.

Also, this property, along with the sums and multiplications one, means something quite amazing: you can figure out ANY logarithm for any combination of fractions, using as a start ONLY the logarithms of prime numbers on a common base. Using the logarithm base 2 of 3 and 5 I could find out log base 15 of 27, for example!

Yeah, this blew my mind too. Anyway, now to figuring out what the other lines do!

Anyway, while working on this I found out a few neat properties of logarithms!

For instance, log a / log b = log base b of a. I have no axiomatic proof of this (yet) but it appears to work fine.

Also, this property, along with the sums and multiplications one, means something quite amazing: you can figure out ANY logarithm for any combination of fractions, using as a start ONLY the logarithms of prime numbers on a common base. Using the logarithm base 2 of 3 and 5 I could find out log base 15 of 27, for example!

Yeah, this blew my mind too. Anyway, now to figuring out what the other lines do!

Posted: **Mon Oct 07, 2013 5:06 pm**

Um... doesn't it equal log (a-b)? Logarithms aren'trobly18 wrote:Alright, I made a better prototype. However, a calculator and paper aren't what you'd call accurate when it comes to placing the numbers in the right spot.

Anyway, while working on this I found out a few neat properties of logarithms!

For instance, log a / log b = log base b of a. I have no axiomatic proof of this (yet) but it appears to work fine.

Also, this property, along with the sums and multiplications one, means something quite amazing: you can figure out ANY logarithm for any combination of fractions, using as a start ONLY the logarithms of prime numbers on a common base. Using the logarithm base 2 of 3 and 5 I could find out log base 15 of 27, for example!

Yeah, this blew my mind too. Anyway, now to figuring out what the other lines do!

(log a) / (log b)

= log a * log -b

= log (a - b)

[[edit: Or not. I fail at remembering stuff]]

Posted: **Tue Oct 08, 2013 7:45 am**

No, I think you got it backwards. Log a - Log b = Log (a/b), not the other way around. In fact, just under the article you sent me, there's "Change of base"

log base b of x = log base k of x / log base k of b

This, coupled with the multiplications, which lets you figure out log base k of b based on it's prime factors, lets you figure out any log on any fractionary base using merely a table of logs with the primes.

Unrelated: In regards to your signature, don't slow down! Forums like these are better off with movement!

The mathemathics are messed up, cleaned up version:The logarithm logb(x) can be computed from the logarithms of x and b with respect to an arbitrary base k using the following formula:

\log_b(x) = \frac{\log_k(x)}{\log_k(b)}.\,

log base b of x = log base k of x / log base k of b

This, coupled with the multiplications, which lets you figure out log base k of b based on it's prime factors, lets you figure out any log on any fractionary base using merely a table of logs with the primes.

Unrelated: In regards to your signature, don't slow down! Forums like these are better off with movement!

Posted: **Tue Oct 08, 2013 4:29 pm**

Oh whoops. Meh, they both have subtraction and divisionrobly18 wrote:No, I think you got it backwards. Log a - Log b = Log (a/b), not the other way around. In fact, just under the article you sent me, there's "Change of base"The mathemathics are messed up, cleaned up version:The logarithm logb(x) can be computed from the logarithms of x and b with respect to an arbitrary base k using the following formula:

\log_b(x) = \frac{\log_k(x)}{\log_k(b)}.\,

log base b of x = log base k of x / log base k of b

This, coupled with the multiplications, which lets you figure out log base k of b based on it's prime factors, lets you figure out any log on any fractionary base using merely a table of logs with the primes.

Unrelated: In regards to your signature, don't slow down! Forums like these are better off with movement!

*thinks*

OH That's right, you use division to change base, just like multiplication to change bases! Which is why I always end up typing log(x)/log(2) into my calculator.

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Ok