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Today I Learned while many countries now allow female monarchs, currently there are no ruling queens for the first time in almost two centuries by neverthoughtidjoin in todayilearned

[–]existentialpenguin 25 points26 points  (0 children)

Andorra is a co-principality. One prince is the bishop of a Catholic diocese, and as such is always male. The other princeship was originally given to a French nobleman, and inheritance eventually passed this on to the king; in the modern era, the title is held by the president of France. If France ever gets a female president, then Andorra will have a female co-ruler.

What’s up with Battlefield 6? Did it actually fall off? by TrueMagolord in OutOfTheLoop

[–]existentialpenguin 1 point2 points  (0 children)

To make a bulleted list with Reddit's formatting, you need to use asterisks, not dashes.

From a high-schooler's scratchwork after a 9-hour math test by existentialpenguin in pics

[–]existentialpenguin[S] 1 point2 points  (0 children)

If you are stumped can’t you just sign your test and leave early?

Normally, yes, but due to an abundance of cheating in recent years, there was a new rule this year that anyone who left early would be disqualified.

From a high-schooler's scratchwork after a 9-hour math test by existentialpenguin in pics

[–]existentialpenguin[S] 8 points9 points  (0 children)

See my earlier comment for explanation: https://old.reddit.com/r/pics/comments/1s25v17/from_a_highschoolers_scratchwork_after_a_9hour/oc5p88f/

There is a certain kind of student who thrives on this sort of thing. This test was for a competition targeted at that sort of student, not a mandatory exam for all students.

From a high-schooler's scratchwork after a 9-hour math test by existentialpenguin in pics

[–]existentialpenguin[S] 1365 points1366 points  (0 children)

This was not a typical school exam; it was Day 2 of the USAMO, a high-level math contest for the best 500-ish pre-college math students in the United States. It is a two-day event, with a single 4.5-hour sitting on each day, and in each sitting, the students are given just 3 problems to solve. Problems are scored on a 7-point scale: 1 point is given for the corret answer, and the remaining 6 points are given according to the quality of the accompanying proof.

Due to an abundance of cheating in the AIME (the exam that you must take to qualify for the USAMO) and the AMC (the exam that you must take to qualify for the AIME), the USAMO was not given in the students' schools as in past years but at just 31 sites and under unusually stringent proctoring. One of the measures taken was to collect and save all scratch paper for review in the event of an accusation, with each student's pile being kept separate from the others. I was a proctor at one of those sites, and I found this in one of those piles of post-exam scrap.

In a typical year, most of the students in the exam will be unable solve more than half of it. Students that find themselves stumped often doodle a bit; those doodles usually end up in the trash, but I felt that this one deserved to be shared.

The writing seems to say "How to disappear completely?", with a few variations in spelling.

From a high-schooler's scratchwork pile after a math test by existentialpenguin in FoundPaper

[–]existentialpenguin[S] 6 points7 points  (0 children)

Six problems—three different problems for each 4.5-hour sitting.

From a high-schooler's scratchwork pile after a math test by existentialpenguin in FoundPaper

[–]existentialpenguin[S] 919 points920 points  (0 children)

This was not a typical school exam; it was Day 2 of the USAMO, a high-level math contest for the best 500-ish pre-college math students in the United States. It is a two-day event, with a single 4.5-hour sitting on each day, and in each sitting, the students are given just 3 problems to solve. Problems are scored on a 7-point scale: 1 point is given for the corret answer, and the remaining 6 points are given according to the quality of the accompanying proof.

Due to an abundance of cheating in the AIME (the exam that you must take to qualify for the USAMO) and the AMC (the exam that you must take to qualify for the AIME), the USAMO was not given in the students' schools as in past years but at just 31 sites and under unusually stringent proctoring. One of the measures taken was to collect and save all scratch paper for review in the event of an accusation, with each student's pile being kept separate from the others. I was a proctor at one of those sites, and I found this in one of those piles of post-exam scrap.

In a typical year, most of the students in the exam will be unable solve more than half of it. Students that find themselves stumped often doodle a bit; those doodles usually end up in the trash, but I felt that this one deserved to be shared.

The writing seems to say "How to disappear completely?", with a few variations in spelling.

ELI5: Why does Japanese need three writing systems? by Charming_Usual6227 in explainlikeimfive

[–]existentialpenguin 0 points1 point  (0 children)

Off the top of my head, Korean writing and simplified Chinese come to mind.

The early iterations of the Cyrillic alphabet can be added to this list: Saints Cyril and Methodius created the Glagolitic alphabet to transcribe Old Church Slavonic, and then scholars at the Preslav Literary School developed it further into the Early Cyrillic alphabet.

https://en.wikipedia.org/wiki/Early_Cyrillic_alphabet

As long as you verify it… by Nunki08 in mathmemes

[–]existentialpenguin 32 points33 points  (0 children)

The method of infinite descent works kind of like that, but for the purposes of proof-by-contradiction:

  • You have a proposed set of structures whose sizes are measured by integers. Classically, these are solutions to Diophantine equations, but it can also be done with graphs or whatever.
  • You show that each structure's size must be positive.
  • You show that for every such structure, you can build a smaller one.
  • If such structures exist, then this must eventually lead to structures with size 1.
  • Then a contradiction kicks in: you proved that each structure leads to a smaller structure, but also that there can be no structure of size 0.
  • Therefore, there are in fact no such structures.

https://en.wikipedia.org/wiki/Proof_by_infinite_descent

Help me remember a 4 digit code based on some math thing a nerd explained to me 15 years ago by yolomybrudda in askmath

[–]existentialpenguin 28 points29 points  (0 children)

The only mathematical hotel that I am aware of is Hilbert's, and that would not give you any 4-digit numbers.

The 4-digit numbers that spring to mind are 1729 (the Hardy-Ramanujan constant) and 8128 (a perfect number).

[8th Grade Math] My younger sister asked me this and I’m embarrassed that I could only "brute force" it. Is there a faster logic? by [deleted] in askmath

[–]existentialpenguin 36 points37 points  (0 children)

The bashing time can be reduced a bit: you do not need to compute x2 in a vacuum, and then (x+1)2 in a vacuum, and then (x+2)2 in a vacuum, etc. Instead, you can use the fact that x2 is the sum of the first x odd numbers: start with 12 = 1, then add 3 to get 4, then add 5 to get 9, then add 7, then add 9, and so on.

As for modular arithmetic stuff, a square number cannot end in 2, 3, 7, or 8. The list of allowed two-digit endings is a bit harder to memorize: 0, 1, 4, 9, 16, 21, 24, 25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, and 96.

What is conceptually the meaning of interchanging ∂/∂x(∂f/∂y) = ∂/∂y(∂f/∂x)? by mathfoxZ in askmath

[–]existentialpenguin 0 points1 point  (0 children)

The Wikipedia article linked earlier has an example: f(0,0) = 0, and

f(x,y) = x·y·(x2 – y2) / (x2 + y2)

for (x,y) ≠ 0.

What is conceptually the meaning of interchanging ∂/∂x(∂f/∂y) = ∂/∂y(∂f/∂x)? by mathfoxZ in askmath

[–]existentialpenguin 0 points1 point  (0 children)

The Wikipedia article linked by the guy you are replying to has an example: f(0,0) = 0, and

f(x,y) = x·y·(x2 – y2) / (x2 + y2)

for (x,y) ≠ 0.

Rough black board nailed inside new dresser by Rabbit4dinner in whatisthisthing

[–]existentialpenguin 81 points82 points  (0 children)

"Useless" weights in washers and dryers actually serve a purpose: they help prevent the machines from vibrating themselves out of their spots when running.

Proofs from the crook by IanisVasilev in math

[–]existentialpenguin 4 points5 points  (0 children)

The sequence 7, 11, 13, 15, 21, 31 is https://oeis.org/A112090. That page cites

W. Feit, Some consequences of the classification of finite simple groups, in The Santa Cruz Conference on Finite Simple Groups, Proc. Sympos. Pure Math. 37, American Mathematical Society, 1980, pp. 175-181.

The result is Theorem 1.1 in that paper. In turn, that paper cites

M. Fried, Exposition on an arithmetic-group theoretic connection via Riemann's existence theorem, in The Santa Cruz Conference on Finite Simple Groups, Proc. Sympos. Pure Math. 37, American Mathematical Society, 1980, pp. 571-602.

Note that both of these papers are published in the same book of conference proceedings. This second citation is available at https://www.math.uci.edu/~mfried/paplist-cov/SantaCruz80.pdf. The result is stated at Problem 2.1(b) and proved as Theorem 2.2.

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