#Math Lessons

[mathsprogram]

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[dekariosclan]

Gale Math

So, we all know that in the epilogue, Gale tells Tav:

I love you.

And if you look at the datamined dialog files and read the dev notes, you’ll see this:

Devnote: With the warmth of having said this a thousand times before.

So, taking that statement as a FACT (which, you know, I’m certain it was intended to be…) we now have a solid numerical value to start with: 1000.

Next, we know that per the narrator at the epilogue start, it’s been 6 months since the defeat of the netherbrain; therefore it’s been 6 months since Gale and Tav got engaged/agreed to live together. We’re going to conclude that they have spent every day together since then.

6 months = 182.5 days

Now, assuming that Gale says ‘I love you’ to Tav on a relatively similar schedule each day (ex: when they first wake up, when Gale heads out to Blackstaff Academy, etc. etc.) we can make an equation:

1000 declarations of love divided by 182.5 days = the amount of times Gale tells Tav he loves them every single day.

We solve the equation and get 5.47945205

We round that down, and voila! We now have flawless mathematical proof that

Gale says ‘I love you’ to Tav an average of 5 times every single day

[locusfandomtime]

Doing the maths: Grian's failure at getting a mending book

lots of talk about maths and probabilities below the cut! but there's a graph and simple explanation at the end if you want to get the gist of it and are bad at maths.

(I am still young and learning maths, critique/advice always welcomed)

What are the odds of getting a mending book in Minecraft?

(I am assuming Grian has been doing all his fishing with Luck of the Sea 3)

The probability of a mending book is actually a bit annoying to estimate. The Minecraft Wiki lists fishing up an enchanted book as 1.9% chance. This is for ANY enchanted book. The Minecraft wiki talks about how the chance of an enchantment being selected is calculated. Mending has a weight of 2. Using the table, mending has a probability of 2/135.

However, Grian is looking for any book with mending, not just a pure mending book. Additional enchantments are calculated in a different way, involving RNG, which means it won't be as easy to model. Due to this reason, I'll just be using the odds for a pure mending book throughout.

TLDR: a mending book has a 0.028..% chance (2/135*0.019*100)

Grian's Data

According to this screenshot, Grian has used a fishing rod 5679 times. This number may not be fully accurate, as it includes the times he's fished other players, rather than just fished for items, but it is a good estimate.

To help visualise this data, with a median waiting time between catches of 17.5 seconds, Grian has spent over 20 hours fishing so far! He may have a problem.

Is this statistically significant?

Hypothesis testing (p-value approach):

H0: p = 19/67500 (the null hypothesis - he has no mending books because of chance)

H1: p < 19/67500 (the alternate hypothesis - he has no mending books due to different odds)

5679 trials, 0 mending books

X ~ B(5679, 19/67500) (binomial distribution, 5679 tries with a probability of a mending book being 19/67500, where X is the number of mending books)

p(X=0) (what is the probability the number of mending books being 0)

p = 0.2021473392

Now, the point at which data becomes significant is subjective. For instance, you *could* get a million heads in a row flipping a coin, it's not impossible, but at a certain point, you can begin to say "okay there's something not normal about this". For this approach, the closer the p-value is to 0, the more evidence there is against the null hypothesis . The p-value here is far above a significance level of 0.01, or 0.05, or 0.1. There isn't a clear line between significant/non-significant, but this is answer is quite a bit far from 0

With this, I cannot reject the null hypothesis.

Personal conclusion: this is not statistically significant, Grian is just unlucky.

Are other values statistically significant?

Gem's proposed 9000: results in a p-value of 0.079... more significant than Grian's number but I don't imagine Mojang would be too concerned. As said though, it's all subjective.

I am bad at maths, what does all this mean?

Here is a graph, showing what number of mending books you might have after 5679 tries. The height of the bar represents the probability of getting that amount. The numbers at the top are the (rounded) numbers I used in my calculation

The pink column is 0 mending books - like what Grian has! As you can see, it is less likely than getting 1 or 2 books, but not too uncommon to happen.

End conclusion: Grian has bad luck. Like, not as hilariously bad as he thinks, but still bad. If he keeps going, chances are he will get a mending book, but I think he should probably stop fishing because at this point he has a problem.

[palermok]

hehehehehehe

[chickensauras]

Very pragmatic. Excellent problem solving skills

[sharky66]

Long lekku for the win!

[simplydnp]

who's hand is in this picture?

A Mathematically Rigorous Proof That I Spent Too Long Writing

welcome to university math: dnp hand edition

(no, don't leave, you'll be fine i promise)

to begin, we need a statement to prove. we have two options:

- the hand is dan's hand

- the hand is phil's hand

now, for most proofs in university math, you are told a true statement, and you must show why it is true using logic rules, definitions, and theorems. but, we do not know which of these statements are true, so we have to find out.

to prove that a statement is true, we must show that it is always true for the situation presented. to show a statement is false, we must present a single instance where the statement is false (also known as a counter example).

a quick not scary math example:

definition: a prime number is only divisible by 1 and itself.

statement: all prime numbers are odd

(this is false, because 2 is a prime number and it is even. you don't even need to check if there's any others, all you need is one single case where it isn't true to disprove it)

so now that we have a little background on proofs and how to prove and disprove them, we go back to our two statements.

the thing with this situation is, one of them must be true (unless you're gung-ho on someone else holding dan's face while phil takes a picture on his phone of dan in his glasses, in which case, i applaud your commitment, but in actuality this proof will cover that option too)

the full statement we have is: dan is touching his face or phil is touching dan's face

now, because this is Real Life and we have a picture where a hand is touching dan's face, we know already that one of these options is true (as mentioned above) but! using symbolic logic you could also come to this conclusion.

this type of statement is an 'or' statement, and if you're curious, you can look into 'truth-tables' and see why, but at least one of the options must be true.

back to the proof at hand (bah-duhm-tss)

okay. now, proofs also must be 'general' in order to mean anything, really. these are statements of truth of the universe, not just for individuals. so, we will prove this generally.

we have 2 people involved, so individual 1 (dan, the owner of the face and potential face toucher) will be labelled as 'D' , and individual 2 (phil, the possible face toucher who does not own the face) will be labelled as 'P'. thus, this can be true for any such D and any such P.

so with our 'or' statement, in order to prove it, we pick one of the options and say that it is not true, and we have to show then that the other is true.

step 1: let's assume this is not P's hand. (assumption)

step 2: thus, it must be D's hand. (what we take from our assumption)

step 3: now, if it is D's hand, we look at what a hand on one's own face is capable of appearing like. (a definition or true fact about step 2)

the position in the given photo shows the hand with a thumb on the cheek, and a finger on the forehead. so, we find an example of a person with their fingers in the same position (or close to) and see if this supports our claim.

consider:

now, with this image, you can clearly see how the subject's right hand has the thumb on the temple and index finger on the top of their head, however, it is a close enough position for our case.

from the view of the camera, the closest finger to the camera is the edge of the pinkie. in fact, it will always be the closest finger to the camera in this position, assuming the subject has all fingers and no additional appendages.

step 4: we now compare this to our photo (we verify if this holds to our claim or contradicts it)

in our photo, the closest appendage to the camera is the edge of the thumb.

step 5: thus, it cannot be the case that D is touching their own face. (what the evidence says)

step 6: as we assumed it was not P's hand and have shown it cannot be D's hand, and as this is an 'or' statement both of these claims cannot be false, we can therefore conclude it must be P's hand. (our conclusion: re-stating the statement and assumptions and conclusion)

step 7: we verify that P is true (optional step but in beginner proofs you generally show why your case works)

to do this, i will show a picture of a person touching another's face, and compare it to our image.

consider:

now, this image is not exactly the same, similar to above. however, P's left thumb is on the cheek, with their index on D's temple. the closest appendage to the camera (if it were in a similar perspective as our original) would be the edge of the thumb.

comparing it to our original:

our comparison holds.

thus, we can conclude that the true claim in this statement is that P must be touching D's face, which, in particular means that:

phil is touching dan's face in the image

thank you for partaking in phannie mathematics. we now know. i am not sorry.

bonus:

phil has a hitchhikers thumb and dan doesn't so why was this necessary at all 🤡

[awesomecooperlove]

😢😢😢FUTURE GENIUSES 😢😢😢

👨🏼‍🎓👨🏾‍🚒👮🏻‍♀️

[ezralva]

This time Together with Maman as school teachers

Caption "Teachers for subjects you're not good at"

What subjects will they teach?

[alphaclxwn]

Glad that you liked drawing that. What are your top five pairings since those three are part of it? Doesn't have to be in a specific order.

1)noaheather

2)alenoah

3)codsay

4)gwody

5)gwendsay

hhshhshshe thanks for asking anon!! i love sharing my ships!!!

[mathsprogram]

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[sspicat]

Too busy with study. I will have to recreate my schedule.. so yk.. For now have this poorly drawn Arcky.

math... my head hurts... i don't want to do maths.

[candycane969]

Not my silly ass making my own fanart instead of writing chapter 3 if you ever wondered how the readers drawings/famous "daddy?" drawing looked like then it might have been like thiss tee hee. my math notes look exactly the same (donatello included)

[ddarker-dreams]

I know you were simplifying exponents in that one ask bc who cares tbh but as a math brained idiot I am compelled to confess that it made my blood boil when you said a number cubed is the same as a number multiplied by three. otherwise I love you and your work is always a treat okay bye 🩷

DID I GET IT WRONG ?????????? my math grades were always 📉 for a reason. english and history had sore backs from carrying my high school GPA. forgive me math anons .... i'll just let my explanation be "something something big number chrollo weird."

[romanceyourdemons]

whenever i go to a boba place and they’re speaking mandarin behind the counter there’s a part of me that thinks i could do it, i could be the white boy who SHOCKS staff by ordering in FLUENT CHINESE. but first of all why would i do that. whom does that help. and second of all i don’t know how to say 70% in mandarin which means i would need to get full-sweetness milk tea and i’m not strong enough for that

[themsthenow]

All based on uzi's og height