Wikipedia:Reference desk/Archives/Mathematics/2017 April 9

= April 9 =

"Thirty days hath February ..."
This website claims:

"A year is known as 365 days, but the earth actually takes 365.25 days to orbit the sun. This is why we had to come up with a leap year every 4 years, to account for the extra .25 that is otherwise not accounted for. Most people are aware of that, but did you know that once every 400 years we also do another leap year in addition? This is because the earth rotates around the sun a little over 365.25 times, just a fraction if you will. We compensate that by having another leap year every 400 years."

A claim frequently encountered is that when Julius Caesar reformed the calendar he gave the odd months 31 days and the even ones thirty and that when Caesar Augustus reformed it he jealously swiped a day from February, added it to Augustus so that his month would be as long as Julius', and then rearranged the lengths of September onwards so that there would not be three successive months of 31 days. How knowledgeable are people about the way the calendar actually works? 86.137.87.214 (talk) 14:13, 9 April 2017 (UTC)
 * By what metric? --jpgordon&#x1d122;&#x1d106; &#x1D110;&#x1d107; 14:43, 9 April 2017 (UTC)
 * And hasn't a similar question been on the ref desk twice already, if my memory hasn't failed me? Double sharp (talk) 14:52, 9 April 2017 (UTC)
 * Yes, it has (one, two). Double sharp (talk) 14:55, 9 April 2017 (UTC)


 * The quote from the website mentioned by the OP is wrong. We don't add an extra leap year every four hundred years. Instead, we subtract a leap year in every year that is divisible by 100 but not by 400. And Earth rotates slightly less than 365.25 times per year. See Leap year. Loraof (talk) 15:16, 9 April 2017 (UTC)
 * Earth does rotate more then 365.25 times a year. It's the precession of the equinoxes and the orbit undoing one turn that makes it less than 365.25. Sagittarian Milky Way (talk) 19:19, 9 April 2017 (UTC)
 * "...the orbit undoing one turn...." You're talking about the number of rotations relative to the distant stars being greater. But we're talking about the number of rotations relative to the Sun. If that were more than 365.25, we would have to have more than one leap year per four years, not less than as we actually have. Loraof (talk) 21:28, 9 April 2017 (UTC)
 * Relative to the Sun isn't real. It's only used because sidereal clocks and calendars that track the movement in inertial space have limited utility. Observatories actually have sidereal clocks. They go up to 23:59:59. Sagittarian Milky Way (talk) 04:37, 10 April 2017 (UTC)
 * The sidereal day is actually 23:56:04 (to the nearest second). Loraof (talk) 13:48, 10 April 2017 (UTC)
 * No they don't go up to ~23:56:04 then roll over. Those are solar seconds. The point of sidereal clocks is to show the currently highest right ascension so they go up to 24 o'clock = 0 o'clock. Then 00:00:01 or infinitesimally close to zero if it's a continually moving second hand. A mundane European clock can be used if you can find a way to make it run 3 minutes 56 seconds fast. Sagittarian Milky Way (talk) 17:42, 10 April 2017 (UTC)
 * I have used the contact form on the website to send a correction. It varies whether sites react to corrections. PrimeHunter (talk) 16:26, 9 April 2017 (UTC)
 * The website links to another one which also contains howlers.  It says, for example, under the heading "Don't the Greeks do it differently?":

"Every year which when divided by 900 leaves a remainder of 200 or 600 is a leap year. ..."

"However, this rule is not official in Greece."

Wrong (notwithstanding the emphasis). This website doesn't have a contact form but it does say here that the writer can be emailed. As I don't have email can someone pass on the information? 86.137.87.214 (talk) 10:22, 10 April 2017 (UTC)


 * The revised Julian calendar is a thing. It's official in the Greek Orthodox Church I think and it won't be till March 0, 2800 AD when the Greeks will have to pick one. Sagittarian Milky Way (talk) 17:47, 10 April 2017 (UTC)
 * And even then it will just oscillate between being exactly aligned with the Gregorian calendar and being one day out; it's not until AD 5200 that it will start being permanently out. The first time it'll be two days out is AD 6400; the first time it'll be three days out is AD 10000, following Sagittarian Milky Way's linked article. Double sharp (talk) 12:45, 11 April 2017 (UTC)
 * Thanks, everyone.  My point was that it's wrong to say that this calendar is not official in Greece (as here for example and no doubt in other places as well).   Back in the seventeenth century the Protestant states of Germany decided to introduce a new calendar.   They objected to Gregory's, so they left it to the Church to formulate a new one and then introduced what they came up with. 86.137.82.110 (talk) 15:31, 11 April 2017 (UTC)

What is a polyomino??
Most sources I've read say (including Wikipedia) say a polyomino must be made out of squares and that a polyform is a more general term. However, this source:

https://books.google.com/books?id=gVJqCQAAQBAJ&pg=PA423&lpg=PA423&dq=%22triangular+polyominoes%22&source=bl&ots=HUE1T2ab83&sig=gbP4ufrGJYQBuZj56izvJKV0l9M&hl=en&sa=X&ved=0ahUKEwjXv9b8gpjTAhWr6YMKHbtMBwcQ6AEIMTAD#v=onepage&q=%22triangular%20polyominoes%22&f=false

uses "polyomino" to mean any polyform. It says that the definition of a polyiamond is a triangular polyomino. Any thoughts here?? Georgia guy (talk) 18:42, 9 April 2017 (UTC)


 * It may cause confusion so I wouldn't give it high marks for writing style, especially if there's no compelling reason, but there are no dictionary police that come after you if you don't conform to the usual meanings of terms. --RDBury (talk) 07:26, 10 April 2017 (UTC)


 * The first sentence in the intro (p. 418) of your linked source defines them in terms of squares. Then p. 419 defines a "triangular polyomino" "consistent with the previous definition" in terms of triangles. So in the absence of a modifier it defines them in terms of squares, and then modified by "triangular" it becomes something analogous. Loraof (talk) 17:35, 12 April 2017 (UTC)
 * But if "triangular" is an adjective that modifies polyomino, then it makes sense that a triangular polyomino is a kind of polyomino, right?? Georgia guy (talk) 13:48, 13 April 2017 (UTC)


 * It "modifies" it in the sense of changing it. Here's an analogy. In the Euclidean plane, does a triangle have straight line segments as sides? Yes. But a Reuleaux triangle does not. Loraof (talk) 14:11, 13 April 2017 (UTC)
 * A Reuleaux triangle is something that contrasts with a Euclidean triangle, which is the kind of triangle we usually think about. There are different kinds of triangles; the Euclidean is simply the most common kind. But with polyominoes, a polyomino is made of squares by definition. Its use in the phrase "triangular polyomino" implies that a definition of a polyomino (even if not the usual one) is any polyform. Georgia guy (talk) 14:43, 13 April 2017 (UTC)
 * Meanwhile, a dwarf planet is not a planet, and a skew field is not a field. Double sharp (talk) 15:04, 13 April 2017 (UTC)