Wikipedia:Reference desk/Mathematics

Average dates

(This is not a homework.)

How to calculate average of dates of recurring events whose dates cannot be pre-determined, such as weather events like first day above 10°C or melting of snow? For example, if some event has happened on 5 March in 2026, 28 February in 2025, 3 March in 2024 and 4 March in 2023, how to calculate the average of these dates in these four years? Does it involve taking ordinals of these days in a common year? --40bus (talk) 06:57, 5 March 2026 (UTC)

I don't know if there is a standard way of doing this. One thing you can do is first convert the dates to fractions by dividing their ordinal positions in their year by the number of days in that year. 4 March 2023 was the 63rd day in a year of 365 days, resulting in 63/365 ≈ 0.1762. 3 March 2024 was also the 63rd day, but now in a year of 366 days, so its fractional value equals 63/366 ≈ 0.1721. Then compute the average of all these fractions, for the example approximately 0.1704. Since most years are common, multiply this by 365 to get an ordinal position, about 62.20. After rounding this corresponds then to 3 March. (In a leap year the expected ordinal position is 0.1704 × 366 ≈ 62.38, corresponding to 2 March.)  ​‑‑Lambiam 08:22, 5 March 2026 (UTC)

Leap years cause a problem here, since if you compute the average number of days from the start of the year then converting that into a date is going to depend on the year. For example the 100th day of 2026 is April 10, but the 100th day of 2028 is April 9. So I think you have to expect an error on the order of a day no matter what. That being said, spreadsheet programs typically have a host of built-in time and date related functions to help streamline date computations. For example in LibreOffice Calc I created a column for the input dates, a column for the year using the YEAR(date) function, a column of the first of the year as =DATE(year,1,1), and a column for the number of days since Jan 1 using DATEDIF. Note that the program stores dates as real numbers with the day (since some global start date) being the integer part. So you can get the difference in days between two dates as just the difference. You can now just take the rounded average of the last column, add that to Jan 1, and call that the average date. FWIW I got Mar. 3. --RDBury (talk) 15:00, 5 March 2026 (UTC)

If a majority of the sampled years are leap years, this may result in 1 January being the average date of the New Year's Eve events.  ​‑‑Lambiam 22:35, 5 March 2026 (UTC)

Well, in the many New Year's Eve celebrations I've been involved in, the festivities have usually extended well into 1 January – quite how far is usually lost in the alcoholic mists, but in some cases actually into 2 January. {The poster formerly known as 87.81.230.195} ~2026-76101-8 (talk) 16:10, 6 March 2026 (UTC)

It may depend on context; for example, in climatology, one might want to translate from calendar dates to something like "days after the solstice" or "days after the vernal equinox"; see e.g. https://www.realclimate.org/index.php/archives/2020/04/nenana-ice-classic-2020/ --JBL (talk) 00:54, 7 March 2026 (UTC)

One could translate dates to Sun-Earth vectors and average the latter. —Antonissimo (talk) 21:35, 9 March 2026 (UTC)

The angular speed of the Earth around the Sun is, by Kepler's laws, inversely proportional to the square of the distance, which, at aphelion, is about 3.4% larger than at perihelion. This would mean that dates around 4 July (aphelion) get almost 7% more weight than days around 3 January (perihelion). The sampled event dates would need to be widely dispersed for this to be of noticeable influence, though, in which case the notion of an average date for the event probably makes little sense.  ​‑‑Lambiam 10:10, 10 March 2026 (UTC)

I think for your purposes of calculating per-year-based data, you'll want to do directional statistics over something like ${\displaystyle e^{2\pi it/T}}$ where ${\displaystyle t}$ is the time of your event as measured from a reference epoch (if you're working from dates alone, pick a standard time of day to place them) and ${\displaystyle T}$ is the length of a year.

This is closely related to the orbital vector calculation someone else suggests. The downside is that going back to dates won't be as nice, but if you ignore the 400-year part of the cycle you can roughly get dates based on leap/first after/second after/third after as your estimate. Sesquilinear (talk) 20:33, 11 March 2026 (UTC)

Consider an event taking place on 1 January in common years but on 31 December in leap years. (So the 2024 event takes place 730 days after the 2023 event, but the 2024 and 2025 events take place on subsequent days. The directional average will then point at 1 January instead of 1 March.  ​‑‑Lambiam 23:04, 11 March 2026 (UTC)

I think trying to track that as a yearly event should give you an average pointing somewhere near the New Year. Imagine observing those events from the perspective of someone using a calendar that instead started near the (Northern Hemisphere) summer solstice. It wouldn't read as something that happened once a year except on average. Sesquilinear (talk) 23:37, 11 March 2026 (UTC)

Are there different methods for an elliptic curve point to a suitable hyperelliptic curve cover than Weil descent?

I ve a curve defined on an extension field but with a point whoes coordinate lies in the base prime field (same coordinate as the prime field version of the curve).

As you know, in the case of applying index calculus, this is largely regarded as impossible as the Weil descent decrease the prime degree (which simplify discrete logarithms computations). But are there really no other methods to lift suchs points to an hyperelliptic curve?

My purpose would be for pairing inversion. I m meaning I can invert type 3 pairings on hyperelliptic curves, so it would be usefull in terms of computational Diffie Hellman if I can move the computations of pairings from bn or bls curves to hyperelliptic curves. ~2026-11394-20 (talk) 23:13, 8 March 2026 (UTC)

Ignorant Monty Hall

Imagine you're faced with a Monty Hall problem, but unlike in the canonical example, the host is ignorant. (In other words, as far as the host knows, #3 could have been the car.) When he asks you whether you want to switch from 1 to 2, is your chance of winning at all affected by the choice? I know the correct answer for the canonical problem is "yes, switch", but I've never understood why, so I don't know whether the host's ignorance would affect the answer. Nyttend (talk) 06:53, 12 March 2026 (UTC)

An easy way to analyze the problem is as follows. We assume that the initial placement is random and that the contestant had rather win a car than a goat. Before any doors are opened, there are three placement patterns with equal probabilities:

1. C G G
2. G C G
3. G G C

Because of the perfect symmetry we may restrict the analysis, without loss of generality, to the case that the contestant initially picks door 1. The contestant knows at this point that the probability there is a car behind the chosen door is 1 in 3; if they further completely ignore what the game host is doing and stick to their guns whatever, they'll end up going home with the big prize with probability 1/3. In the original problem, with an informed game host, the latter now has the choice of opening either door 2 or door 3. Again, without loss of generality, assume they open door 3. The contestant should realize that if they don't switch, their chance of winning is (as we saw before) unaffected: it is still 1/3. Since the car is not behind door 3 and the probabilities need to still add up to 1, the initial 2/3 probability of doors 2 and 3 combined remains now with door 2 alone.

With an ignorant game host, opening door 3 and revealing a goat eliminates pattern 3. We have, by symmetry, with equal probabilities:

1. C G G
2. G C G

Clearly, there is no point in switching. This is in fact the naive analysis most people apply to the original Monty Hall problem, not taking into account that in the setting the game host is careful not to open the door with a car behind, breaking the naive symmetry.  ​‑‑Lambiam 08:48, 12 March 2026 (UTC)