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March 27

Good resource for 3D dynamics

I want something that satisfies the following.

Covers inertia tensors, equations of motion, angular velocities, working from body-fixed frames etc.
Is free and can easily be downloaded.

I do not want discussions of Hamiltonian or Lagrangian mechanics: I want something basic to simply set problems up. I'm not too clear on all the rules for rotational dynamics. The focus is more engineering than physics incidentally; however, I am not interested in homogeneous coordinates.--Leon (talk) 19:30, 27 March 2019 (UTC)[reply]

You can read Rigid_body_dynamics. Ruslik_Zero 13:08, 28 March 2019 (UTC)[reply]

March 28

A (probably) simple problem in plane differential geometry

Take a plane, smooth, non self-intersecting curve C and a circle of fixed radius whose center moves along C. Suppose that C always cuts the circle in two simply connected regions of equal area. Is it true that the curve must be a straight line?

93.150.177.220 (talk) 18:34, 28 March 2019 (UTC)[reply]

I would think so. The slightly weaker statement where we require this to hold for circles of arbitrarily small radius is definitely true (since an arbitrarily small circle can be fit to only enclose a part of C that is strictly concave or convex). It is also true for when C has everywhere nonzero curvature. The only difficult case is when C has zero curvature at some point within every possible placement of the circle. I'm not sure how to prove it rigorously but I think using some calculus of variations would go a long way. We could pick a parametrization of C, when the difference between the two regions' areas is then a functional of the parametrization of C. It would then be sufficient to show that when the parameter is arc length, the second derivative vanishes (equivalent to zero curvature).--Jasper Deng (talk) 20:08, 28 March 2019 (UTC)[reply]

I doubt the fact that the result is intuitive makes it a simple problem. Especially when it comes to differential geometry, where the obvious statement "a closed continuous non self-intersecting curve divides the plane into an interior and an exterior" is devilishly difficult to prove. Tigraan^{Click here to contact me} 12:59, 29 March 2019 (UTC)[reply]
- I think the Jordan curve theorem is not so difficult if limited to smooth curves (like in the OP's question), polygonal paths, or whatever. The difficulty comes from pathological nowhere-differentiable curves and stuff like that. 67.164.113.165 (talk) 15:58, 2 April 2019 (UTC)[reply]

~~The answer is "no". Consider for example radius $2\pi$ and curve $y=\sin(x)$ .~~ Sorry, that doesn't work. However, I see no reason to believe that it couldn't be tweaked to give something that does work. --JBL (talk) 00:51, 3 April 2019 (UTC)[reply]

March 31

846

Is the number 846 possible or necessary? DuncanHill (talk) 22:25, 31 March 2019 (UTC)[reply]

Yes, it exists. 846 seconds is less than a quarter of an hour. 846 inches is just over 70 feet. Georgia guy (talk) 01:03, 1 April 2019 (UTC)[reply]

I think 846 is possible, but not necessary. I've never used it. Bubba73 ^{You talkin' to me?} 03:42, 1 April 2019 (UTC)[reply]

Let's abolish all unnecessary numbers (as determined by Bubba's Criterion). Then we can really get down to business solving the mysteries of the universe without all that impedimenta blocking our view. -- Jack of Oz ^{[pleasantries]} 08:38, 1 April 2019 (UTC)[reply]

Courtesy links: 846 (number), 846 (year), oeis. --RDBury (talk) 09:55, 1 April 2019 (UTC)[reply]

Courtesy link: The Birthday Party (play). -- ToE 02:22, 2 April 2019 (UTC)[reply]

846 is a great number!

It is one of the numbers n such that n^16 + 1 is prime.

It is one of the number of benzenoids with 21 hexagons with C_(2v) symmetry containing n carbon atoms.

The original NAND gate was a DTL chip by Motorola, the MC846.

It is one of the multiples of 6 containing a 6 in their decimal representation.

It is one of the composite numbers in which all substrings are composite.

There is a two-dimensional cellular automaton defined by "Rule 846", based on the 5-celled von Neumann neighborhood.

21 U.S. Code § 846 says that "Any person who attempts or conspires to commit any offense defined in this subchapter shall be subject to the same penalties as those prescribed for the offense, the commission of which was the object of the attempt or conspiracy."

The Resource Conservation and Recovery Act (RCRA) governs waste management and materials recovery and reuse, including the disposal of both hazardous and non-hazardous solid waste. In support of RCRA, EPA developed test methods for the analysis of various environmental media. These test methods can be found in the EPA publication, Test Methods for Evaluating Solid Waste: Physical/Chemical Methods, also known as SW-846.

See [ https://oeis.org/search?q=846&fmt=short for an additional ] 704 fascinating things about the number 846

Also see [ https://xkcd.com/2016/ ].

--Guy Macon (talk) 01:11, 5 April 2019 (UTC)[reply]

April 1

Find three integers $n_{1},n_{2},n_{3}$ such that $n_{1}^{3}+n_{2}^{3}+n_{3}^{3}=42$

I tried to find a solution to $n_{1}^{3}+n_{2}^{3}+n_{3}^{3}=42$ for $n_{1},n_{2},n_{3}\in \mathbb {Z}$ using a computer program, but so far I haven't found a solution. Count Iblis (talk) 03:37, 1 April 2019 (UTC)[reply]

I got it, but it is too large to type in. :-) Bubba73 ^{You talkin' to me?} 03:41, 1 April 2019 (UTC)[reply]

According to this article, this is an unsolved problem. The corresponding problem for 33 instead of 42 has just been solved and involves 16-digit numbers. --76.69.46.228 (talk) 05:44, 1 April 2019 (UTC)[reply]

There is a Numberphile video on this as well. Happy April 1 folks! --RDBury (talk) 09:33, 1 April 2019 (UTC)[reply]

Compounding & smoothed values

Hi, I have a maths problem which I can't figure out how to resolve, though it might be fairly simple to the users on here.

I have a set of values which increase by 125% every 25 days. As follows:

Number of days	Value
Day 0	50
Day 25	112.5
Day 50	253.125
Day 75	569.53125
Day 100	1281.445313
Day 125	2883.251953

and so on...

This is all the information we have, and that the data would follow a smoothed upward trajectory. My question is how I predict a value which is not a multiple of 25. For example how do I predict what the value would be on day 120, according to the pattern of this data? Uhooep (talk) 10:17, 1 April 2019 (UTC)[reply]

@Uhooep: The formula for exponential growth is

x_{t}=x_{0}(1+r)^{t}

= 50×(1 + 125%)^day/25 = 50×2.25^day/25. After 120 days it is {{#expr:50*2.25^(120/25)}} = 2451.5801216619. PrimeHunter (talk) 10:52, 1 April 2019 (UTC)[reply]

I wonder who was the first to discover the well known formula of the Sine (or the Cosine or the Tangent) of sum of angles.

HOTmag (talk) 12:56, 1 April 2019 (UTC)[reply]

See History of trigonometry. --JBL (talk) 14:03, 1 April 2019 (UTC)[reply]

Thx. HOTmag (talk) 13:20, 2 April 2019 (UTC)[reply]

April 2

Wikipedia:Reference_desk/Archives/Mathematics/2018 June 23#Bathroom tiling question...

The following question was asked twice before but was archived before answer (once after 7 hours and once after 13):

I subscribe to a faculty mathematics journal. I am reminded of a puzzle I saw there which remains the only one which nobody has submitted an answer to. Can the Wikipedia experts do better?

A year-to-view calendar has the months in a conventional arrangement of three months in each of four rows. The names of the months are printed as normal, but the days (Sunday to Saturday) and the dates (1 to 28, 29, 30, or 31 as the case may be) are printed on removable tiles. You can choose from 1x1 squares (for a single month), 1x2 rectangles (for two adjoining months in a single row) or 1x3 rectangles (covering the whole row) and both sides of the tiles are available for printing. What is the minimum number of tiles you need to print up to ensure your calendar can be used in any year?

- 86.155.146.159 16:47, 30 June 2018

Supplementary question:

Assume the tile area covered by the display for a single month to be 1 unit, irrespective of the number of tiles printed what is the minimum number of units required to ensure your calendar can be used in any year? There may be a direct relationship to the minimum number of tiles required - I don't know if there is or not. 86.130.156.147 (talk) 12:33, 17 February 2019 (UTC)[reply]

I presume that we need to work out what variations we have in months. There are obviously a set of 7 with the first of the month on each day of the week. Then there are 28, 29, 30 and 31 day months, so we need 28 (7*4) different 1x1 tile-faces (perhaps only 14 double sided tiles). But we may need multiple copies of the tiles (we will only ever need one copy of the 28 and 29 day months - February. Duplication needs thinking about, but simplistically there are 4 30-day months (sep apr jun nov) and 7 31-day months (jan mar may jul aug oct dec). Therefore 7 * (1 + 1 + 4 + 7) 1x1 tile faces = 91. Therefore 46 1x1 tiles is sufficient, but can they be reduced by mixing starting day of week within each year (yes) and by merging adjacent months into 1x2 or 1x3 tiles (yes). That last sentence needs thinking doing. But your answer is "less than 46 tiles". -- SGBailey (talk) 10:41, 3 April 2019 (UTC)[reply]

Why do you want a calendar in your bathroom?

Some years ago, when in hospital, I went to the bathroom one morning and noticed a laminated piece of paper on the floor propped against the wall. Picking it up, I saw it was a year-to-view calendar printed from the timeanddate.co.uk website. Large areas of the world don’t have access to the internet, let alone printers and laminating machines, so a calendar you don’t throw away would be extremely useful (as it would be everywhere, for environmental reasons). Lamination is also to be discouraged because it generates plastic. Can anyone estimate the total weight of calendars currently binned each year?

As for duplication, in a common year October is a duplicate of January and in a leap year there are no duplications at all.86.146.195.49 (talk) 08:19, 4 April 2019 (UTC)[reply]

I can get it down to 18 1x3 double sided tiles. 7 do Mon thru Sun, Jan thru Mar, non leap one side and leap other side. Then the remaining 9 months are 7+7+7 tilefaces which can be squeezed onto 11 tiles. -- SGBailey (talk) 08:39, 4 April 2019 (UTC)[reply]

Now, you've eliminated the need for duplicate faces because the tiles needed for January and October are separate. I would have thought, therefore, that April to December could be squeezed onto only seven tiles (Sunday to Saturday, beginning each day of the week), with a 31-day month on one side and a 30-day month on the other. Can the fronts and backs be judiciously arranged so that the tile which has a particular 31-day month on the front does not display a 30-day month on the back which is required in the same year? 86.146.195.49 (talk) 09:00, 4 April 2019 (UTC)[reply]

Hold on! Obviously you can't cover nine months with only seven tiles. Could you do January and February on their own and arrange the other eleven tiles somehow to cover March to December? 86.146.195.49 (talk) 09:05, 4 April 2019 (UTC)[reply]

April 4

hi, ive post something abt some possible solution polynomial time for discrete logarithm problem

Suposing it works well n suposing i got some other ideas that i tried also put them here n there on this internet thing...

my question it will be why do i have to feel so odd abt nobody encourages me to keep doing this kinda things as for edu research

anyway just a small crisis of mine, at the bottom of this

thank You, Florin Florin747 (talk) 19:39, 4 April 2019 (UTC)[reply]

Mathematical Symbol for Irrational numbers? FalloutCraftr! (talk) 01:15, 5 April 2019 (UTC)

Hello! I am wondering if there is a symbol or word that represents all irrational numbers, like the Aleph-naught, which represents all real numbers. I am also wondering if there is a symbol like it for imaginary numbers.

@@ Line 158: / Line 158: @@
 thank You, Florin [[User:Florin747|Florin747]] ([[User talk:Florin747|talk]]) 19:39, 4 April 2019 (UTC)
+== Mathematical Symbol for Irrational numbers? [[User:FalloutCraftr!|FalloutCraftr!]] ([[User talk:FalloutCraftr!|talk]]) 01:15, 5 April 2019 (UTC) ==
+Hello! I am wondering if there is a symbol or word that represents all irrational numbers, like the Aleph-naught, which represents all real numbers. I am also wondering if there is a symbol like it for imaginary numbers.