# Math cube root **URL:** \ **Category:** Ruby\ **Created:** [July 11, 2009, 12:48pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915 "2009-07-11T12:48:40Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 12:48pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/1 "2009-07-11T12:48:40Z")
Hi, Is there a cube root (as [Cube root - Wikipedia](http://en.wikipedia.org/wiki/Cube_root)) function in Ruby? Math module seems not offer it… except a Math.sqrt(). Thanks. ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 1:07pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/2 "2009-07-11T13:07:05Z")
def cube\_root(x) Math.exp(Math.log(x.to\_f)/3.to\_f) end Cheers, Serabe P.D. Proof: Cube root of x is equal to x^(1/3) x^(1/3) = y ln(x^(1/3)) = ln y (1/3)ln x = ln y Ergo y = e^((ln x)/3) ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 1:10pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/3 "2009-07-11T13:10:00Z")
So, so sorry. Even easier. def cube\_root(x) x\*\*(1/3.0) end Cheers, Serabe ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 6:45pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/4 "2009-07-11T18:45:22Z")
2009/7/11 Fabian S. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid): > but nice math anyways 🙂 Four years studying maths at the university should be useful for something, should’nt it? 🙂 Cheers, Serabe ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 9:11pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/5 "2009-07-11T21:11:26Z")
one might argue that way, I guess _g_ gives me the satisfaction that what I’m getting into my head right now for the next exam is not entirely useless _g_ 2009/7/11 Sergio A. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 6:17pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/6 "2009-07-11T18:17:53Z")
> So, so sorry. > > Even easier. but nice math anyways 🙂 Greetz ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 11, 2009, 10:59pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/7 "2009-07-11T22:59:31Z")
2009/7/11 Zangief I. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) > Hi, > > Is there a cube root (as [Cube root - Wikipedia](http://en.wikipedia.org/wiki/Cube_root)) class Numeric def root(arg) arg\*\*(1.0/self) end end p 3.root 27 p 2.root 9 ## – Thomas P. removed\_email\_address@domain.invalid [http://thopre.googlepages.com/](http://thopre.googlepages.com/) [http://thopre.wordpress.com/](http://thopre.wordpress.com/) Jack Benny [http://www.brainyquote.com/quotes/authors/j/jack\_benny.html](http://www.brainyquote.com/quotes/authors/j/jack_benny.html) “I don’t deserve this award, but I have arthritis and I don’t deserve that either.” ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 13, 2009, 2:17am UTC](https://www.ruby-forum.com/t/math-cube-root/171915/8 "2009-07-13T02:17:32Z")
Hi, Am Samstag, 11. Jul 2009, 19:48:50 +0900 schrieb Zangief I.: > Is there a cube root (as [Cube root - Wikipedia](http://en.wikipedia.org/wiki/Cube_root)) > function in Ruby? Math module seems not offer it… except a > Math.sqrt(). I suppose you mean the method mentioned under “Cube root on standard calculator”. Here’s an implementation: class Numeric def sqrt Math.sqrt self end def cbrt neg = self \< 0 c = abs.sqrt.sqrt i = 2 loop do w = c i.times { w = w.sqrt } i \*= 2 w \*= c break if c == w c = w end neg ? -c : c end end If you like it in C (only Ruby 1.8): [http://bertram-scharpf.homelinux.com:8808/doc\_root/bs-ruby-2.3/rdoc/classes/Numeric.src/M000033.html](http://bertram-scharpf.homelinux.com:8808/doc_root/bs-ruby-2.3/rdoc/classes/Numeric.src/M000033.html) Bertram ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 13, 2009, 8:05am UTC](https://www.ruby-forum.com/t/math-cube-root/171915/9 "2009-07-13T08:05:42Z")
On Jul 11, 3:58 pm, Thomas P. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > ``` > arg**(1.0/self) > > ``` > > “I don’t deserve this award, but I have arthritis and I don’t deserve that > either.” Correction: class Numeric def root(arg); self\*\*(1.0/arg) end end ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [July 13, 2009, 12:47pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/10 "2009-07-13T12:47:59Z")
Thanks you! Thomas P.'s method is perfect. There is no correction to do jzakiya. ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 11, 2011, 9:43pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/11 "2011-05-11T21:43:25Z")
How can you explain this: ``` $ irb 1.9.2p180 (main):001:0> 1000 ** (1.0/3) 9.999999999999998 1.9.2p180 (main):002:0> Math.sqrt(100) 10.0 ``` ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 2:33pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/12 "2011-05-12T14:33:32Z")
On Wed, 11 May 2011 21:45:42 +0200, Sergey Avseyev [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > How can you explain this: > > ``` > $ irb > 1.9.2p180 (main):001:0> 1000 ** (1.0/3) > 9.999999999999998 > 1.9.2p180 (main):002:0> Math.sqrt(100) > 10.0 > > ``` Floating-point numbers have a finite precision. As a result, the outcome of a numerical (computer) calculation usually differs from the outcome of the mathematical calculation. Assume you only can operate with integers and want to compute the square root of 133. You may then end up with either 11 (11² = 121) or 12 (12² = 144) while the actual result is approximately 11.5 (11.5² = 121 + 11 + 0.25 = 132.25; more precisely 11.5325625947). You may like to use formatted output of numbers that suppresses digits beyond the actual precision: jupp@pen2:~ $ irb irb(main):001:0\> “%.15f” % 1000 \*\* (1.0/3) =\> “9.999999999999998” irb(main):002:0\> “%.14f” % 1000 \*\* (1.0/3) =\> “10.00000000000000” The above example turns the numerical value into a string displaying a fractional part with 15 and 14 digits, respectively. Assuming that IEEE 754 double precision floating point numbers (i.e. those used by Ruby) have a precision of a little less than 16 (decimal) digits it is safe to assume that the complexity of operation you perform results in a value that is precise to a little less than 15 digits - which means that you can assume 14 digits to be correct. By chance it MAY be precise to more digits as it is the case for Math.sqrt(100) - but that is nothing you can rely on unless you learn some gory details of numerical mathematics. HTH ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 3:59pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/13 "2011-05-12T15:59:38Z")
On Thu, May 12, 2011 at 8:25 AM, Josef ‘Jupp’ Schugt [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > instead of using floats you can try to use rational numbers in ruby: ruby-1.9.2-p180 :001 \> require ‘mathn’ =\> true ruby-1.9.2-p180 :002 \> 1000 \*\* (1.0/3) =\> 9.999999999999998 ruby-1.9.2-p180 :003 \> 1000 \*\* (1/3) =\> 10 ruby-1.9.2-p180 :004 \> 1.0/3 =\> 0.3333333333333333 ruby-1.9.2-p180 :005 \> 1/3 =\> (1/3) you need to require ‘mathn’ which will change integer division (and make all the numbers play nicely together) but other than that things will work better. the only down side to this whole thing is that rationals are slower than floats (probably significantly so) because it is a pair of integers. and some values when you look at them wont seem to make sense as a rational, like PI: ruby-1.9.2-p180 :011 \> Math::PI =\> 3.141592653589793 ruby-1.9.2-p180 :012 \> Math::PI.to\_r =\> (884279719003555/281474976710656) you can always num.to\_f back but that also takes time. one last thing: if your inputs are floats i’m not sure there is a nice way to convert them to rationals: ruby-1.9.2-p180 :016 \> (1.0/3).to\_r =\> (6004799503160661/18014398509481984) ruby-1.9.2-p180 :017 \> 1/3 =\> (1/3) so this entire e-mail may be moot 😛 hex ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 5:29pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/14 "2011-05-12T17:29:21Z")
On Thu, May 12, 2011 at 2:54 PM, serialhex [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > … > instead of using floats you can try to use rational numbers in ruby: > ruby-1.9.2-p180 :001 \> require ‘mathn’ > which also changes this: > (-1) \*\* (1.0 / 3) #=\> NaN > to: > (-1) \*\* (1.0 / 3) #=\> (0.5+0.866025403784439i) > so we can also get complex roots if we want them! > … > one last thing: if your inputs are floats i’m not sure there is a nice way > to convert them to rationals: > (1.0/3).to\_r #=\> (6004799503160661/18014398509481984) > I think that is a nice way! It’s telling us (I think) what is the > exact rational represented by the float. After all, a float is just a > special type of rational, or rather floats are a subset of the subset > of the rationals defined by them have powers of two as denominators in > their representation using the smallest positive denominator. (I hope > that’s correct.) Whether it’s a _good_ idea to be able to convert floats to “ordinary” rationals is another question, and I’m sceptical about that: I think one should probably only want to do it if one fully understands floating point representation, and if one fully understands floating point representation, I suspect one wouldn’t want to do it! ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 8:33pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/15 "2011-05-12T20:33:41Z")
On Thu, May 12, 2011 at 10:26 AM, Colin B. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid)wrote: > Which we don’t here, given that the cube root of -1 isn’t imaginary 😕 ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 11, 2011, 10:07pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/16 "2011-05-11T22:07:31Z")
On 5/11/2011 14:45, Sergey Avseyev wrote: > How can you explain this: > > ``` > $ irb > 1.9.2p180 (main):001:0> 1000 ** (1.0/3) > 9.999999999999998 > 1.9.2p180 (main):002:0> Math.sqrt(100) > 10.0 > > ``` You’re using floating point arithmetic which is always inexact. The 1.0/3 part cannot be represented with infinite precision, so it’s basically rounded at a certain point. The result is then used for the rest of the operation, which may compound the inaccuracy introduced by the initial rounding. If you must use floating point operations, be prepared to accept results that are only _close_ to what you expect, where close is largely dependent on the operations being performed. > **[Floating-point arithmetic](https://en.wikipedia.org/wiki/Floating_point)** > > In computing, floating-point arithmetic (FP) is arithmetic that represents a subset of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. > Numbers of this form are called floating-point numbers.: 3 : 10  > For example, 12.345 is a floating-point number in a base-ten representation with five digits of precision: > However, 12.3456 is not a floating-point number with five base-ten digits of precision. > In practice, most floatin... -Jeremy ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 8:53pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/17 "2011-05-12T20:53:29Z")
On Thu, May 12, 2011 at 2:30 PM, Josh C. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > Which we don’t here, given that the cube root of -1 isn’t imaginary 😕 there are actually 3 cube roots of -1 (and 4 quad roots of -1, and 5 penta roots of -1 and…) behold the code: ruby-1.9.2-p180 :004 \> a = (-1)**(1/3) =\> (0.5000000000000001+0.8660254037844386i) ruby-1.9.2-p180 :005 \> a.conj =\> (0.5000000000000001-0.8660254037844386i) ruby-1.9.2-p180 :006 \> a.conj**3 =\> (-1.0-3.885780586188048e-16i) ruby-1.9.2-p180 :007 \> a\*\*3 =\> (-1.0+3.885780586188048e-16i) ruby-1.9.2-p180 :008 \> (-1)\*\*3 =\> -1 (conjugation simply flips the sign of the imaginary number, which is helpful for a bunch of things) so while there may be 1 _real_ root for a given number, there are n roots for any number taken to the (1/n)th power. and while most people will want the (simple) (-1)\*\*(1/3) == (-1) answer, they are all right (minus the floating-point rounding errors… which is kind of odd cause i would think that i would be getting the rational representation of the complex numbers instead of floats… idfk… whatev!) hex ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 8:57pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/18 "2011-05-12T20:57:11Z")
On May 12, 2011, at 2:30 PM, Josh C. wrote: > > to: > > (-1) \*\* (1.0 / 3) #=\> (0.5+0.866025403784439i) > > so we can also get complex roots if we want them! > > Which we don’t here, given that the cube root of -1 isn’t imaginary 😕 ONE of the cube roots of -1 isn’t imaginary, but the other two are. Since (1.0/3) isn’t exactly one-third, raising -1 to (1.0/3) isn’t exactly the same as taking the cube root either. -Rob Rob B. removed\_email\_address@domain.invalid [http://AgileConsultingLLC.com/](http://AgileConsultingLLC.com/) removed\_email\_address@domain.invalid [http://GaslightSoftware.com/](http://GaslightSoftware.com/) ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 10:31pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/19 "2011-05-12T22:31:48Z")
On May 12, 2:53pm, Rob B. [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > > On Thu, May 12, 2011 at 10:26 AM, Colin B. \ > > > > (-1) \*\* (1.0 / 3) #=\> (0.5+0.866025403784439i) > > > Rob B. > > > removed\_email\_address@domain.invalid [http://AgileConsultingLLC.com/](http://AgileConsultingLLC.com/) > > > removed\_email\_address@domain.invalid [http://GaslightSoftware.com/](http://GaslightSoftware.com/) See my Roots Module. > It allows you to easily (and accurately) get all n values for a root n, for all number classes. Instead of: 1000 **3** -1 of 1000\*\*(1.0/3) to get only default root Instead do: 1000.root(3) or 1000.roots(3), for all 3 cube roots Jabari Zakiya ---
**Author:** ![z4n9ief](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/z/7993a0/32.png) [@z4n9ief](https://www.ruby-forum.com/u/z4n9ief)\ **Post date:** [May 12, 2011, 10:36pm UTC](https://www.ruby-forum.com/t/math-cube-root/171915/20 "2011-05-12T22:36:44Z")
On Thu, May 12, 2011 at 4:25 PM, jzakiya [removed\_email\_address@domain.invalid](mailto:removed_email_address@domain.invalid) wrote: > See my Roots Module. > [roots.rb · GitHub](https://gist.github.com/422636) spiffy!!! hex [Next page](https://www.ruby-forum.com/t/math-cube-root/171915.md?page=2)