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May 27

Significance of the multiplicative digital root

The digital root is an interesting property of a natural number. The sequence of digital roots of natural numbers will always follow a pattern that repeats every ninth cycle. It can be used in determining whether a number is divisible by 3 because 3 is a factor of 9. But how about the multiplicative digital root?? I don't see how it's interesting. One property is that almost all natural numbers that are not made entirely out of 1's will have a multiplicative digital root of 0, which means that I don't see how this property of a number is interesting. Georgia guy (talk) 14:34, 27 May 2016 (UTC)[reply]

There's a lot of properties of numbers that I don't personally find interesting, yet for some reason they still have WP articles! Ok more seriously did you look at this [1] ref to math world? Looks like several OEIS sequences are touched upon, people are interested in how long it take the sequence to get to zero, Erdos did some stuff with it. The refs there also might be "interesting" to some, e.g. this thread [2] on "zero-length messages". SemanticMantis (talk) 15:11, 27 May 2016 (UTC)[reply]

Deriving the volume of a box from only two linear measurements

This seems intuitively correct to me. If you have a right rectangular prism, with sides of the lengths a, b, and c, and the space diagonal d:

d={\sqrt {a^{2}+b^{2}+c^{2}}}.\

and you know the lengths from a to a' and the length of the diagonal segment d, can you not determine the volume of the cuboid from just those two measurements alone, without needing to measure the actual length of the b and c segments?

When I envision this in my head, if the lengths of the a and d segments are constant, then you can rotate the box about the a axis, but the volume will remain constant.

Assuming my visual intuition is true, and you've gotten the lengths of the a and d segment by tape measure (a large empty fishtank is what brought up this question in my mind), what would the equation for the volume be, using only those two variables.

Thanks, μηδείς (talk) 22:32, 27 May 2016 (UTC)[reply]

Doesn't work. You get the same d value, for boxes with a fixed a length, for a range of volumes of box. Consider boxes of roughly 1, 0.5, 1.3229, and 1, 0.1, 1.4108. Same d value. Different volumes - .66 & .14. --Tagishsimon (talk) 22:43, 27 May 2016 (UTC)[reply]

Okay, so you picked a d value of the square root of three and worked backwards. I should have thought of that, but I haven't started with the yield and worked backwards to the reagents since HS. Thanks. μηδείς (talk) 00:09, 28 May 2016 (UTC)[reply]

To put Tagishsimon's observation more explicitly and generally: Knowing a and d gives you b²+c², but what you need is bc. —Tamfang (talk) 08:10, 28 May 2016 (UTC)[reply]