I found complex roots of a polynomia,l one being (0.5, sqrt7) but the problem says to find all solutions to said polynomial in mod7. There is only one real solution to this, which is easy to take mod7 since its an integer, but what happens when I have a complex number with 0.5 as a real part? My guess its not possible since 0.5 is not an elemnt of mod7, is that right?
I’ve recently stumbled upon the “frog riddle” from TED-Ed and I also saw that it has been repeatedly discussed here on r/math and elsewhere before.
I’d like to share my views on why I think it’s so controversial and present a modified (corrected) version which should capture the essentials of the original.
From my point of view there are two reasons why the riddle is so controversial:
- it tries to illustrate a quite unintuitive aspect in probability
- it includes some small errors which actually make the riddle unfit for this demonstration
Below there’s a short version of the original as well as an addition I’ve come up with that I would say fixes errors of the original.
You can also watch the original here: https://www.youtube.com/watch?v=cpwSGsb-rTs
The riddle (modified version)
You are in the rainforest looking for a female frog of a specific species. In this species the share of males and females is 50% each, and the males and females are indistinguishable to the eye. However, there are two other ways to actually tell them apart:
- on occasion (but very rarely) male frogs will give off a very distintive croak. Females don’t give off any sounds
- male frogs also have a specific smell. If you are closer than 1 meter to a male frog you’ll be able to smell it
Now, consider two scenarios:
- scenario 1: you hear the croak of a male frog and follow it towards a spot where you see two frogs sitting next to each other
- scenario 2: you walk around the rainforest until you notice the smell of a male frog. You look around and see two frogs sitting next to each other close to you.
Now, what’s the likelihood of one of the frogs being a female in either scenario?
- in the scenario in which you hear a male frog the chance of also finding a female is 1 / 2
- in the scenario in which you smell a male frog the chance of also finding a female is 2 / 3
My reasoning is:
The following combinations of frogs occur with the same likelihood: ff, mf, fm, mm. So, we could assume there are just those 4 pairs of frogs in the rainforest (4 males and 4 females in total)
If you follow the call of a male frog you will find any of the four male frogs with the same likelihood. I’m indicating each of the male frogs you can find with a capital letter here: Mf, fM, Mm, mM. Therefore there’s a 25% chance of finding the mf pair, a 25% chance of finding the fm pair and a 50% chance of finding the mm pair.
If you walk around until you smell a male frog, your chances of finding either of the mf, fm or mm pair are equal. You’re not more likely to find the mm pair. So there’s a ~33% chance for each, resulting in a ~67% chance for finding a female.
What are your thoughts? I’m confident I got it right, but I’d appreciate hearing others’ thoughts and comments!
Why are so many prime numbers in powered arithmetic series. I will tell you what I mean.
12 … 22 … n2, take any n and (n+1), determine n2 + (n+1)2, chances are you are looking at a prime. It depends on the range, if you look at the range of 1 million to 2 million, you can find half a million odd number with 70000 primes. So the prime percentage is very low(14%). But if you calculate n= 1001 through 1225 you can find many primes with small number of guesses, so chance of prime is like 18% here(for example 10002 + 10012 =2002001 is a prime).
Now, this applies for n3 and n4 (and higher order) series as well, in 13 23 33 n3 series, for any n and n+1, (n+1)3 – n3 likely to be a prime, percentage depends on the range though. This is even better as you can find 45 primes in 245 searches(for 1 mil to 2 mil range), so percentage is 22%. For neven you usually have to sum up numbers and for nodd you have to substract from next number. For n4 series, I calculate the percentage is 40% (2 primes in 5 check).
So my question is wut is going on here. I have watched this video https://www.youtube.com/watch?v=HvMSRWTE2mI but can you please elaborate the cause of this? I am not a mathematician I don’t understand this things well. Explain to me like I am fourteen.
Moreover what is the meaning of these patterns in a more philosophical/geometrical sense? Does this mean if I construct a cube then place it in slightly bigger cube(+1 meter in each direction), the difference(annulus) will likely be a prime number? And if I take a circle in 0,0 coordinate in a paper and the circle goes through any point x,y where difference x~y=1; the circle’s radius is likely be a prime or something? Or am I reading into this too much?
Also, can somebody elaborate the early prime finders’ methods or something? the video link I mentioned, is this time of powered equation concept a recent discovery? For 150years, 5 hundred thousand was the biggest prime, and then Euler came, what equation did he use, why couldn’t he figure out bigger prime number than 2.5 billion? I mean he could have just played with equations like n4 or n5 right?
Also, when I was using my program, I noticed for some higher order, none of the integer outputs are divisible by 5, which was strange to me, I mean they are divisible by 7 17 37 etc but almost never by 5, rarely by 3. Although this could possibly be explained by coefficient rules like a3+3a2 +3a+1 or something (my brain stopped working).
This may sound dumb, but I’m looking for an equation to relate the side lengths of a right triangle with an angle other than the right angle without trigonometry. In other words, I’m wondering how trig functions in a calculator actually work. For example, take this triangle: https://imgur.com/a/ZPyMptr From this we know angle 2 is 45. Using the sine function we know that the length of side b is 3. However, this requires a calculator, and from my (limited) knowledge a calculator “draws out” the unit triangle to get the ratio of the side lengths. I was wondering how I’d do this on paper (without actually drawing it out, of course). Is there an equation to get the ratio of the sides from an angle other than the right angle in a right triangle?
I am currently an eighteen year old high school graduate and will be attending a online college come next year. But throughout my entire student career I had excelled in every class except math and science with the later being so required in the first place that had I not lived in Texas as a homeschool student I most likely would’ve had to repeat high school. Lately I’ve been using khan academy to do simple things like multiplication which I knew I am bad at but i noted that I’m doing it everyday so it’s getting easier for me math is about challenging yourself but most people my age can do algebra and calculus by this time I cannot do that as of now.I have large gaps in my knowledge that began at 3rd grade so what problems should I try to work on in such a way that it would prepare me for more advanced forms of mathematics? It’s starting to be something that I’m starting to enjoy doing so it’s something I’d like to get better at if I can