Masthash

#math

Felipe Kinoshita
3 hours ago

Fixed a few things in my mathematical logic REPL and added some documentation explaining the different operators and propositions, you can try it out here!

https://git.sr.ht/~fhek789/malo#malo

#math #computerscience #logic

LeRoy Miller
5 hours ago

speed nerdlegame 690 solved in 0m 55s!

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LeRoy Miller
5 hours ago

Mathle 686 4/5
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Hourly Hectoc Bot
6 hours ago

Greetings fellow humans,
A new hectoc for you:

155891

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

log(😅 )=💧 log(😄 )
#math #meme

Courtney Cantrell
9 hours ago

Spouse is helping 11yo with her #math homework

Him: Okay, so how would you start solving this problem.

Her *thoughtfully*: ...Not do it?

I mean, I can't blame her.

Math is hard for us #ADHD brains.

#DAVE
#DopamineAttentionVariabilityExecutivedysfunction

Patrick Honner
10 hours ago

Preparing my lesson for Monday's #geometry class.

Me: In 150 words or less, prove that a quadrilateral with a right angle is a square.

ChatGPT:
If a quadrilateral has a right angle, consider the diagonals and opposite angles. Let ABCD be the quadrilateral with a right angle at, say, angle ABC. The opposite angles, like ABC and ADC, are supplementary due to the right angle. Now, examine the diagonals AC and BD. The diagonals bisect each other at right angles, forming congruent triangles ADC and ABC by Side-Angle-Side. This implies that AD is congruent to BC. In a quadrilateral with right angles and congruent diagonals, it must be a rectangle. But since AD is congruent to BC, the opposite sides of the rectangle are also congruent. Therefore, ABCD is not just a rectangle; it's a rectangle with all sides congruent, meeting the criteria of a square.

#math #geometry #MathEd

Paysages Mathématiques
13 hours ago

"Mathematical discoveries – small or large, and whatever their content [...], are never born of spontaneous generation. They always presuppose a ground sown with prior knowledge, and well prepared [...]" – Théodore Flournoy (1854-1920)
#quote #mathematics #maths #math

Paysages Mathématiques
13 hours ago

"Les découvertes mathématiques – petites ou grandes, et quel que soit leur contenu [...], ne naissent jamais par génération spontanée. Elles supposent toujours un terrain ensemencé de connaissances préalables [...]" – Théodore Flournoy (1854-1920)
#citation #mathématiques #maths #math

Hourly Hectoc Bot
13 hours ago

Greetings fellow humans,
A new hectoc for you:

492464

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

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by @seism0saurus

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Paysages Mathématiques
15 hours ago
Jan :rust: :ferris:
15 hours ago

Me, trying to figure out how to implement basic drag functionality in #Bevy #BevyEngine UI without the cursor jumping to the mid-point of the dragged rectangle.😬

My head hurts!🥴 😪

#Struggle #Learning #Math #Geometry #2D #Graphics

A drawing showing multiple rectangles nested into each other. The most inner rectangle contains a mouse cursor symbol from which different geometric lines originate forming different triangles with the sides of the outer rectangle.
Dave Mark
16 hours ago

There was once an SAT question that no one got right.

See the pic for the question and the 5 choices. NONE of the choices are correct!!!

The video (linked below) walks through the answer, though for extra credit, see if you can work out the correct answer yourself.

Humble brag, I got there! 🏆

Here's a video walking through the solution:

https://www.youtube.com/watch?v=FUHkTs-Ipfg
#Math #Puzzle

Two circles, side by side, the radius of circle A is ½ the radius of circle B.
Starting from the position shown in the figure, circle A rolls around circle B. At the end of how many revolutions of circle A will the center of circle first reach its starting point?
(A)2
(B) 3 (C) 6 (D)
(E) 9
Non-Euclidean Dreamer
16 hours ago

In 2-Adics instead of 3-Adics Collatz looks different...

#math #codeart

Ryan Ruff
17 hours ago

Happy #CategoryTheory #Caturday! This week I continued on through L&S Session 15 by trying to solve Exercise 9 in Python. I managed to reconstruct the original endomaps from the presentation, but I'm still uncertain where my missing two maps are. I was stopped by Edward who insists my #math is up and it's time to commence with the petting of the #cats. Who am I to argue?
https://rruff82.github.io/LS-Categories/session15-p6.html

an orange tabby cat interjects himself between the photographer and laptop
Preston MacDougall
18 hours ago

“The #MATH Myth” debunked on @Wikipedia. 👉 https://en.m.wikipedia.org/wiki/The_Math_Myth

Here in #Tennessee , #PISA scores (National Report Card) rose at the fastest pace of any state ever after we won the ‘Race to the Top’ competition that was used to augment #STEMeducation and implement #CommonCore emphasis on language and conceptual #math. ✅

Then, #BananaRepublicans ‘pulled the rug out’ from under our students, and scores headed #South again.

#SaveAmerica from the #MAGA cult!

José A. Alonso
18 hours ago

Formalizing fundamental algebraic number theory. ~ Anne Baanen. https://cs.vu.nl/~tbn305/publicaties/proefschrift-latest.pdf #ITP #LeanProver #Math

Hourly Hectoc Bot
19 hours ago

Hello math fans,
The hectoc of the hour is:

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The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

José A. Alonso
19 hours ago

Mathematics and the formal turn. ~ Jeremy Avigad. https://arxiv.org/abs/2311.00007 #Math #ITP

José A. Alonso
19 hours ago

Is deep learning a useful tool for the pure mathematician? ~ Geordie Williamson. https://arxiv.org/abs/2304.12602 #AI #Math

José A. Alonso
19 hours ago

Advancing mathematics by guiding human intuition with AI. ~ Alex Davies et als. https://www.nature.com/articles/s41586-021-04086-x #AI #Math

LeRoy Miller
23 hours ago

hard mathler 676 3/6

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Knowledge Zone
23 hours ago

A Century Later, New #Math Smooths Out #GeneralRelativity : Quanta Mag

Is #Technology harming our #Brains? : Medium

#ChatGPT for #Chemistry: #AI and #Robots join forces to build new materials : Nature

Check our latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

LeRoy Miller
23 hours ago

Numbword #485 100/100

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"I really think types are the fundamental currency of Java, not strings."
- Crazy Bob Lee

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LeRoy Miller
23 hours ago

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Paysages Mathématiques
1 day ago

9 décembre 1883 : #CeJourLà naissance de Nikolaï Louzine (†28/1/1950), mathématicien russe dont les travaux portent en particulier sur la théorie des ensembles, l'analyse (cf. théorème de Lusin) et la topologie.
https://fr.wikipedia.org/wiki/Nikola%C3%AF_Louzine
#mathématiques #maths #math

Hourly Hectoc Bot
1 day ago

Hi!
The hectoc of the hour is:

777982

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

#math question: why does the nth triangular number equal n+1 choose 2? e.g. how does each dot in the diagram above T(4) corresponde to a choice of 2 things from a set of 5 things?

LeRoy Miller
1 day ago

speed nerdlegame 689 solved in 2m 4s!

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🟩 🟪 ⬛️ Instant Nerdle 675 solved in 1m 14s!

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LeRoy Miller
1 day ago

Mathle 685 4/5
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Hourly Hectoc Bot
1 day ago

Hello everyone,
Your hourly hectoc is here:

959211

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

MathOutLoud
1 day ago

Today we’re asked about the topologist’s sin curve. See my thought process and solution here:

https://youtu.be/zQvDvRnVg4c

#math #mathematics

Flipboard Science Desk
1 day ago

Can AI teach math teachers how to improve student skills?

@TheConversationUS explores the question: https://flip.it/vZMtL7

#AI #Math #Maths #Education #Teachers #Tech

Paysages Mathématiques
2 days ago

"Les mathématiques sont la plus belle et la plus puissante création de l'esprit humain. Les mathématiques sont aussi anciennes que l'Homme." – Stefan Banach (1892-1945)
#citation #mathématiques #maths #math

Paysages Mathématiques
2 days ago

"Mathematics is the most beautiful and most powerful creation of the human spirit. Mathematics is as old as Man." – Stefan Banach (1892-1945)
#quote #mathematics #maths #math

The King
2 days ago

We can generalize the "use n propositions to split into 2^n lemmas" even further. We can split on infinitely many propositions at once!

Let I be a set with an element representing each proposition (i.e. it's an index set) and T⊆I represent the set of true propositions. Generally, I will be simple (such as the set of natural numbers) but we don't know how to nor do we need to calculate T (since they are unknown propositions).

Let's say you want to use the trick to prove A⇒B.

Here's what you need to prove:

> Let S denote an arbitrary subset of I.
> Assume A and that S⊆T (i.e. that S is a set of true propositions).
> Prove that ((exists x. x∈T\S) or B).

This represents our "2^n lemmas", if we count each S as a separate lemma!

The intuition is that we start with S=∅, and use the lemma to keep adding true propositions to it everytime we hit the first case. Eventually we either hit the second case of the lemma result, or we eventually build up to S=T (and then we must hit the second case).

Proof of A⇒B using the lemma

The actual proof is much simpler though and doesn't use any kind of recursion. Just let S=T in the lemma! (We could've actually done that to start with, but the intuition works better if we think of S as being any subset of I.) We have A and that S⊆T, so we can use the lemma. There are two cases:

- exists x. x∈T\S: Since, T\S=T\T=∅, we have a contradiction. By the principle of explosion, conclude B.
- B: We conclude B.

Therefore B.

#constructive #math

Felipe Kinoshita
2 days ago

After almost failing my mathematical logic class I decided to create a little interactive program to help me get better at it!

Uppercase variables are a bit special and get re-evaluated every time you call them.

#logic #math #computerscience

Program running an interactive prompt, commands executed:
proposition p is set to true
proposition q is set to true
proposition uppercase A is set to p and q
proposition A evaluates to true
proposition p is set to false
proposition A evaluates to false
Paysages Mathématiques
2 days ago

8 décembre 1919 : #CeJourLà naissance de Julia Robinson (†30/7/1985), mathématicienne américaine dont les travaux sur le dixième problème de Hilbert (résolution d'une équation diophantienne) ont permis à Y. Matiassevitch de donner une réponse (négative).
https://fr.wikipedia.org/wiki/Julia_Robinson
#mathématiques #maths #math

Paysages Mathématiques
2 days ago

8 décembre 1865 : #CeJourLà naissance de Jacques Hadamard (†17/10/1963), mathématicien français dont les travaux portent sur la théorie des nombres (preuve du th. des nombres premiers), les équations aux dérivées partielles, l'analyse fonctionnelle...
https://fr.wikipedia.org/wiki/Jacques_Hadamard
#mathématiques #maths #math

The King
2 days ago

#constructive #math tip

Often in a proof using classical math, you might take a related proposition X and split into cases "X" and "not X". Some examples in number theory: <https://en.wikipedia.org/wiki/Riemann_hypothesis#Excluded_middle>.

We can't do this in constrictive math, but there is a trick that is equivalent (and more elegant)!

X is any kind of proposition, such as:

- a conjecture, like the Riemann hypothesis
- a statement with free variables, like "n > k" or "G is finite" or any instance of "x has property P"
- a statement independent of your axioms, like the continuum hypothesis or the axiom K

In many cases you might be able to prove excluded middle (EM) for your specific X, but here's an alternative that works for any X.

**The trick**

If you are trying to prove A⇒B, prove the following two lemmas first:

- A⇒(X or B)
- (A and X)⇒B

Classically this is equivalent to splitting on "X or not X" (the first lemma is the "not X" case since "A⇒(X or B)" is equivalent to "(A and not X)⇒B" if EM holds for X), but it's still a theorem constructively that those two lemmas imply A⇒B!

Proof

Assume A. By the first lemma we conclude X or B. There are two cases:

- X: By the second lemma conclude B.
- B: We conclude B.

Therefore B.

If you are just trying to prove C, then use the above trick on "1=1⇒C". If you are trying to refute C, use the above trick on "C⇒0=1". For proof by induction, A can include the induction hypothesis.

Moreover, if you have n propositions of interest, you can split into 2^n lemmas. Adding more propositions never hurts since you can ignore any unneeded propositions when proving any of the lemmas! Many of the lemmas may be trivial or redundant if you already know some relationships between the propositions.

Hourly Hectoc Bot
2 days ago

Greetings fellow humans,
A new hectoc for you:

183379

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

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Hourly Hectoc Bot
2 days ago

Hi!
The hectoc of the hour is:

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The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

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by @seism0saurus

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LeRoy Miller
2 days ago

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LeRoy Miller
2 days ago

Numbword #484 100/100

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LeRoy Miller
2 days ago

🙂Save a par🙂
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LeRoy Miller
2 days ago

speed nerdlegame 688 solved in 1m 29s!

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LeRoy Miller
2 days ago

Mathle 684 2/5
⬜🟨⬜🟩⬜🟨🟩🟨
🟩🟩🟩🟩🟩🟩🟩🟩

mathlegame.com

#mathle #mathlegame #math #game #puzzle

Hourly Hectoc Bot
2 days ago

Greetings fellow humans,
The hectoc of the hour is:

123342

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

Akshar Varma
2 days ago

There is a neat visual proof of this generalized means' inequality using radii, diameter, chords of a specifically constructed circle. In that case, it is visually clear that the inequality holds. However, the fact that specific line segments correspond to the means is hidden behind a few applications of Pythagoras theorem and/or similar triangles.

These "few application of Pythagoras/similar triangles" will result in the exact same formulation as above (and is in fact the inspiration for the above reformulation).
This can be found here: https://commons.wikimedia.org/wiki/File:MathematicalMeans.svg

Another visual proof, in which the inequality is obvious since the line segments are all on the same line is present here: https://commons.wikimedia.org/wiki/File:MathematicalMeans.svg

I like the first proof *slightly* more because the second requires separate coloring/notation to show where each means' line segment starts and ends which the first does not. Although, if that is not an issue and the figure can be produced with enough clarity, then the immediately obvious inequality relationships are a point in favor of the second proof.

#math #inequality #visual #proof

Non-Euclidean Dreamer
2 days ago

Coded up p-Adics, Testing them with Collatz!
#math #codeart

P-Adic representation of positiv integers on a sqrt(3) to 1 rectangle. They take their color when getting iterated with the Collatz rule. In the end we only have a stable zero and the fluctuating 4-2-1
Alfredo
2 days ago

Nerding out on #eigenchris ' wonderful math videos. Just finished the Tensor for Beginners series, going on to Tensor Calculus. Hugely important, as #tensors are the gateway to the theory of #relativity among others. #math #physics
https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG

The answer to 230 - 220 × 0.5 is in fact 5!

#math

Paysages Mathématiques
3 days ago

"It is impossible to be a mathematician without being a poet in soul."– Sofia Kovalevskaya (1850–1891), quoting "one of the leading mathematicians of our century" (probably Karl Weierstrass).
#quote #mathematics #maths #math #poet

Paysages Mathématiques
3 days ago

"Il est impossible d’être mathématicien sans avoir l’âme d’un poète." – Sofia Kovalevskaya (1850–1891), citant "l’un des principaux mathématiciens de notre siècle" (probablement Karl Weierstrass).
#citation #mathématiques #maths #math #poète

Hourly Hectoc Bot
3 days ago

Dear mental calculators,
Your hourly hectoc is here:

179626

The goal is to combine the 6 numbers to a total of 100. You can use the mathematical operations + - * / ^ and the parenthesis ( ). Numbers can be combined, but you have to use all 6 of them and are not allowed to change the order. See https://hectoc.seism0saurus.de for an example. If you want to post a solution, please use a content warning "solution".

Have fun! Your hourly hectoc bot
by @seism0saurus

#math #mentalcalculator #hectoc

Emmanuel José García
3 days ago

The half-angle formulas are central! And as a picture is worth a thousand words...

If you don't know what I'm talking about, read my essay 'The Theoretical Importance of Half-Angle Formulas' and discover the most powerful formulas of all time.

Essay: https://drive.google.com/file/d/1jPrWxUhB1Tnsd5RH5UiMhwmkp2jCv11v/view?usp=sharing

#math #halfangleapproach #symmetrymatters #insight

Rafael
3 days ago

Making salsa from n-dimensional tomatoes

===

I was making salsa the other day and got to thinking about the relationship between how many cuts you make and how many pieces you end up with. It's interesting, right? If I make two cuts through a slice of tomato and the cuts are parallel, I get three pieces but if the cuts are perpendicular, I get four. Same number of cuts different outcome. What's going on? It turns out that it has to do with the dimensionality of tomatoes. 1/x #math #mathstodon

Preston MacDougall
3 days ago

@mythologyandhistory And did you know that this #cartography error led to a parched Peach State *today*?!

"Chemical Eye 👁️ on the Borderline" 👉 http://www.sitnews.us/MacDougall/032208_macdougall.html

#MATH #education #Tennessee #Georgia

José A. Alonso
3 days ago

'A-team' of math proves a critical link between addition and sets. ~ Leila Sloman. https://www.quantamagazine.org/a-team-of-math-proves-a-critical-link-between-addition-and-sets-20231206/ #ITP #LeanProver #Math

José A. Alonso
3 days ago
José A. Alonso
3 days ago

A matroid-based automatic prover and Coq proof generator for projective incidence geometry. ~ David Braun, Nicolas Magaud, Pascal Schreck. https://hal.science/hal-04318847/document #ITP #Coq #Math

David Meyer
4 days ago

The 16th century French lawyer and mathematician François Viète [1] was the first person to discover an infinite product formula for π. Viète's formula, which was the first identity to express π as a limit, was published 1593.

Viète's beautiful formula involves just a single number: 2

There is a nice explanation of how Viète's formula works here: https://steemit.com/mathematics/@nenio/vietes-formula-for-pi.

#pi #math #maths

References
--------------
[1] "François Viète", https://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te

The 16th French lawyer and mathematician François Viète [1] was the first person to discover an infinite product formula for π. Viète's formula, which was the first identity to express π as a limit, was published 1593.

Viète's beautiful formula involves just a single number: 2

There is a nice explanation of Viète's formula here: https://steemit.com/mathematics/@nenio/vietes-formula-for-pi.

#pi #math #maths

References
--------------
[1] "François Viète", https://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te
Ele Willoughby, PhD
4 days ago

For #ArtAdventCalendar Day 6 my #linocut of Marjorie Rice (née Jeuck, 1923–2017) who discovered 4 new pentagonal tilings of the Euclidian plane.

The San Diego mother of 5 (6th died in infancy) completed half a correspondence art course after high school & had no training as a #mathematician but was always interested in #math & art. 🧵1/n

#MastoArt
#womenInSTEM #printmaking #histsci

My linocut portrait of Marjorie Rice with 4 groupings of her 4 pentagonal tiling patterns in pale orange, pink, purple and lime. Her shirt is a pattern of orange butterflies and white daisies on a dark green background. The pattern is based on the orange pentagonal tiling. She is shown in green with a background of yellow at her neckline to lime going up with lines and details overprinted in dark green. She is smiling at the viewer.
José A. Alonso
4 days ago

Concentration inequalities (in Isabelle/HOL). ~ Emin Karayel, Yong Kiam Tan. https://www.isa-afp.org/entries/Concentration_Inequalities.html #ITP #IsabelleHOL #Math

José A. Alonso
4 days ago

Martingales (in Isabelle/HOL). ~ Ata Keskin. https://www.isa-afp.org/entries/Martingales.html #ITP #IsabelleHOL #Math

José A. Alonso
4 days ago

Fermat’s Last Theorem for regular primes. ~ Riccardo Brasca et als. https://github.com/leanprover-community/flt-regular #ITP #LeanProver #Math

U.S. students' #math scores plunge in global education assessment 👇 ✖️ ➗ 🤪

https://www.axios.com/2023/12/05/us-students-pisa-global-assessment

Ed Wiebe
4 days ago

What I do with the students struggling with #math is help them.

I don't usually bother with the #writing unless I cannot understand what they are trying to communicate. There are a lot of students with poor spelling. I think they really have not been exposed to much vocabulary. A lot of students think rain is "percipitation".

We do always see a few students who write libido when they mean albedo. I correct that one.

Petra Schwer
4 days ago

Imagine you had the chance to buy a new blackboard for your office - what would you choose and why?
a) an actual blackboard (with chalk and everything)
b) a glassboard with good markers (tell me your favorite brand)

(please don't tell me how awful whiteboards are. Will not buy one of those anyway)

#math #blackboard #chalk

Dr. Steve Thompson
5 days ago

If we don't see this as a debilitating effect of technology on society through mass consumerism, we may be missing its root.

"U.S. students' math scores plunge in global education assessment"

Meanwhile, the rest of the world can't read anymore...

https://www.axios.com/2023/12/05/us-students-pisa-global-assessment

#math #literacy #technology #society

Flipboard News Desk
5 days ago

U.S. student math scores fall on international test, but many other countries suffered more.

The 74th reports: "The PISA test offers the latest evidence on COVID-related learning loss."

https://flip.it/526djs

#Math #Maths #Education #COVID #Pandemic

David Meyer
5 days ago

Analytic geometry is a fantastic area of mathematics which is populated by all kinds of crazy objects. Being that it is Christmastime (and therefore Christmas math time) please check out the paradoxical object shown on the left. This object is sometimes known as the Infinite Gift. A related object is known as Gabriel's Wedding Cake [7].

In the Infinite Gift the length of the side of the nth box is 1/√n, so the area of one side of the nth box equals (1/√n)² = 1/n. Since a box has 6 sides the surface area of the nth box is 6·(1/n). Then what you find is that in the limit as n → ∞ the Infinite Gift has infinite surface area but finite volume!

Here's an interesting aside: In the limit the area of the Infinite Gift equals 6 times the harmonic series (which we know diverges [8]).

The continuous version of this object is known as Gabriel’s Horn (aka Torricelli’s Trumpet) and is shown in the figure on the right [1,2]. Gabriel's Horn is the surface of revolution of the function y = 1/x about the x-axis for x ≥ 1. As we can see in image, in the limit Gabriel’s Horn has volume = π and area = ∞. These properties lead to an interesting situation known as the Painter’s Paradox [3,4].

This is the Painter's Paradox: Somehow even though you can fill Gabriel’s Horn with paint (its volume is finite), you still won’t have enough paint to cover its inside surface (its area is infinite)!

Merry Christmas everyone!

#christmastimeischristmasmathtime #infinitegift #gabrielshorn
#torricellistrumpet #math #maths #analyticgeometry

(1/2)

The Infinite Gift
Gabriel's Horn
David Colarusso
5 days ago

(3/?) Is it magic? No, it's #math. Yes, we’re talking about unsupervised machine grading. For more nuance than social media can provide, check out the paper with links to code and data here: https://law.mit.edu/pub/unsupervised-machine-scoring-of-free-response-answers/release/1

Slide with icon of a rabbit in a hat and the text, "What sorcery is this?"
Preston MacDougall
5 days ago

@capntransit @csgstewart #Tennessee legislators and #Nashville City Council take note! Widening interstates will NOT solve one of the nation’s worst traffic problems. Only #MassTransit will.

Use #MATH , c’mon man, you can do it!!

"After introducing plural logic and its main applications, the book provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic."

Florio, Salvatore, and Øystein Linnebo, The Many and the One: A Philosophical Study of Plural Logic (Oxford, 2021; online edn, Oxford Academic, 23 Sept. 2021), https://doi.org/10.1093/oso/9780198791522.001.0001, accessed 4 Dec. 2023. #OpenAccess #OA #Philosophy #Language #Maths #Math #Mathematics #Logic #NonFiction #Academic #Book #Books #Ebook #Ebooks #Bookstodon @philosophy @bookstodon (67)

Resolviendo la incógnita
5 days ago

Las funciones trigonométricas seno, coseno, tangente, cotangente, verseno, coverseno, secante, exsecante y cosecante en la circunferencia goniométrica. ¿Las conocías todas? #math #matematicas

Circunferencia donde se van viendo los valores de las distintas funciones trigonométricas.
Adam Coffman
6 days ago

@sc_griffith Pedro the #math cat 🐈🎀 with some snow in his second Winter season ❄️
#cats #CatsOfMastodon

he still hates it
Ronaldo Lobato
1 week ago

A new version of @sagemath was released. Many changes and new contributions.

https://github.com/sagemath/sage/releases/tag/10.2

#math #foss #python #sagemath

ƧƿѦςɛ♏ѦਹѤʞ
1 week ago

@atoponce @phonner
Why do you think that the set of reals has a different size from the set of squared reals?
#maths #math #infinity #yawn

Simple proof that infinities come in different sizes:

lim x->∞ x = ∞(1)
lim x->∞ x² = ∞(2)
∞(2) - ∞(1) = lim x->∞ x² - x = ∞ > 0
QED

#math

Ryan Ruff
1 week ago

It's #CategoryTheory #Caturday again and I'm still stuck on L&S Session 15 Exercise 7! This week I break down my Python code from last week to "solve" Exercise 8, but am still just brainstorming possible solutions for 7. Alphonse is still helping, this time by sitting on the tan cushion which is now back in "ottoman"-form. It seems like a fitting metaphor for my hypothesis about my missing maps somehow. #math #cats https://rruff82.github.io/LS-Categories/session15-p5.html

a photo of a brown tabby cat sitting on a ottoman with tan cushion
Gwen Fisher
1 week ago

By the way, this works.
#math #mathed

8/15 divided by 2/3 equals
(8 divided by 2)/(15 divided by 3) equals 4/5.
ƧƿѦςɛ♏ѦਹѤʞ
1 week ago

@matj1
Only 99%? Really?
154476802108746166441951315019919837485664325669565431700026634898253202035277999,

36875131794129999827197811565225474825492979968971970996283137471637224634055579,

4373612677928697257861252602371390152816537558161613618621437993378423467772036
#maths #math #elliptic
https://math.berkeley.edu/~tb65536/AG_Final_Project.pdf

David Meyer
1 week ago

Did you know that 276,951,438 is the smallest 9-digit number that, when written in three rows of 3, forms a 3×3 magic square?

#math #maths #magicsquare

[Image credit: https://en.wikipedia.org/wiki/Magic_constant#/media/File:Magicsquareexample.svg]

References
--------------
[1] "Magic constant", https://en.wikipedia.org/wiki/Magic_constant

[2] "A006003", https://oeis.org/A006003

[3] "Notes on Magic Squares and Cubes", https://www.trump.de/magic-squares

Did you know that 276951438 is the smallest 9-digit number that, when written in three rows of 3, forms a 3×3 magic square?

#math #maths #magicsquare
matj1
1 week ago
99% of people cannot solve this!
🍎/(🍈 + 🍍) + 🍈/(🍎 + 🍍) + 🍍/(🍎 + 🍈) = 4
Can you find positive whole values for 🍎, 🍈 and 🍍?
Preston MacDougall
1 week ago

@Sheril The solution is simple #MATH : #PrimaryFromTheCenter ! 🤔

C’mon, folks, this ain’t rocket 🚀 surgery!

Christian Lawson-Perfect
1 week ago

Last year, I arranged a series of ten talks by disabled mathematicians, aimed at a general audience.
Presenters included @solderandchaos, @sophiemacmaths, @matthras, and me, roped in at short notice.
The recordings are all still online: https://www.ncl.ac.uk/maths-physics/engagement/outreach/what-can-mathematicians-do-/

If you're starting to put up christmas decorations, my quick explanation of how to fold and cut a Christmas star might inspire you: https://www.youtube.com/watch?v=S90WPkgxvas

#math #maths #WhatCanMathematiciansDo

Paysages Mathématiques
1 week ago

7 of the hardest math problems that have yet to be solved
Source : Interesting Engineering / Tejasri Gururaj

https://interestingengineering.com/lists/math-problems-unsolved-hardest-part1
#mathematics #maths #math #problems

Rémi Eismann
1 week ago

#decompwlj
The decomposition into weight × level + jump of natural numbers is the fundamental theorem of arithmetic ; applied to prime numbers, it leads to a new classification of primes

1000 sequences decomposed with 3D graphs (threejs webGL), 2D graphs - CSV, dump, img to download
⬇️ ⬇️
https://decompwlj.com

➡️ OEISWiki page: Decomposition into weight × level + jump : https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump
➡️ arXiv:0711.0865 [math.NT]: Decomposition into weight * level + jump and application to a new classification of primes: https://arxiv.org/abs/0711.0865

#FundamentalTheoremOfArithmetic #math #maths #mathematics #sequences #OEIS #NumberTheory #PrimeNumbers #JavaScript #php #graph #3D #classification #primes #threejs #webGL #integer #decomposition #arithmetic #numbers #theory #equation #graphs #sieve #fundamental #theorem #arithmetic

Jason Yip
1 week ago

The SAT Question Everyone Got Wrong - YouTube

https://www.youtube.com/watch?v=FUHkTs-Ipfg #math

Garrit ☃️
1 week ago

I just talked to someone who knows #math and I asked them why you can't divide by zero. I feel enlightened. 👀

https://garrit.xyz/posts/2023-11-30-why-you-can't-divide-by-zero

This is post 090 of #100DaysToOffload.

Infinity or division by zero error?
JavaScript or PHP? Pick your side 😜
This is the best mathematical explanation of the "division by zero" problem I've seen, explained by #EddieWoo, watch this: https://www.youtube.com/watch?v=J2z5uzqxJNU

#mathematics #math #programming
#JavaScript
#PHP

JavaScript: division by 0 = Infinity.
PHP: division by 0 has no result, DivisionByZeroError.

"X Value" by @XKCD@ comic - OK... ummm... don't be too quick to depend on a comic strip to do your homework for you. 🤔 https://xkcd.com/2861/ #math #WTF

"Tuple" (in the #Math or #programming context) is pronounced

tom
2 weeks ago

from "Fractal functions and interpolation" by Michael F. Barnsley (1986)

https://link.springer.com/article/10.1007/BF01893434?utm_source=dlvr.it&utm_medium=mastodon

#math #fractal

Wuzzy
2 weeks ago

If a child says that 2+2=22, it's not wrong. It has just done an implicit typecast to string and interpreted the plus sign as a string concatenation operator.

#math #jokes #programming

J Λ M Ξ S
2 weeks ago

📺 What are these strange dice? | Numberphile

If you like TTRPGs and #math, then this vid will be your jam

https://youtu.be/3akBMSJ37Uk

Frozen Canuck
2 weeks ago

Video game developer Freya Holmér has an excellent talk on why you can't multiply vectors. Her talk even includes snail cats and an oracle named Salad!

https://www.youtube.com/watch?v=htYh-Tq7ZBI

#math

Patrick Honner
2 weeks ago

Carmichael numbers, Fermat's Little Theorem, and a remarkable high school student who has etched their name in mathematical history, in my latest column for @QuantaMagazine

https://www.quantamagazine.org/pierre-de-fermats-link-to-a-high-school-students-prime-math-proof-20231122/

#math #MathEd #NumberTheory

Header image for the article "Pierre de Fermat's Link to a High School Student's Prime Math Proof" showing a cartoon Fermat and student working together on a long sheet of mathematical formulas.