Force applied over 2d is N/m^2 = pressure
Force applied over 1d is N/m^1 = tension
Force applied over 0d is N/m^0 = force
Force applied over -1d is N/m^-1 = Nm = torque
Recent searches
Search options
Administered by:
#math
60 posts49 participants9 posts today
"A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all." – Godfrey Harold Hardy (1877-1947)
#quote #mathematics #math #maths
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
The natural numbers (A000027) 
https://decompwlj.com/3DgraphGen/Natural_numbers.html
Theorem of the Day (May 22, 2025) : Irrationality of Circumference of Unit Circle
Source : Theorem of the Day / Robin Whitty
pdf : https://www.theoremoftheday.org/NumberTheory/TauIrrational/TotDTauIrrational.pdf
notes : https://www.theoremoftheday.org/Resources/TheoremNotes.htm#216
A formalization of elementary linear algebra: Part I. ~ David M. Russinoff. https://www.russinoff.com/papers/linear1.pdf #ITP #ACL2 #Math
I just had a case of that weird cognitive dissonance with 3 x 17 = 51.
I was grepping a log and found 51 occurrences of a log message and thought "Aha! Something's wrong!" Then I checked and found there should be 17 triggers, three log messages each time. Everything's fine.
51 *feels* prime. It's just got a primey kinda sheen to it. All lies.
![explanation from explainXKCD https://www.explainxkcd.com/wiki/index.php/3092:_Baker%27s_Units
(truncated to fit)
A baker's dozen is 13 units of bakery goods, as opposed to the normal dozen meaning 12. [...]
Randall proceeds to apply this principle to other things comprised of 12 units, some with bizarre results:
Imperial feet are 12 inches long; a baker's foot would be 13 inches.
Noon is 12:00 o'clock [...]; baker's noon would be 1 o'clock PM ("thirteen hundred hours").
Dodecahedrons have 12 faces (the shape that most d12s take the form of), baker's ones are tridecahedrons (which are not Platonic solids [...]), rendering dice-based games unbalanced.
Years have 12 months; a baker would celebrate New Year's Eve on January 31 [...].
Octaves are comprised of 12 half-steps. A baker’s octave would have 13 half-steps and cause problems in musical composition, [...]
Trial juries in the Anglo-Saxon law tradition consist of 12 peers. The baker’s jury has 13 peers. [...]
The Flag of Europe has 12 stars forming a circle (unlike in the US flag, the stars do not represent member states. The flag was first adopted by the Council of Europe in 1955, when it already had 13 members [...])
Magnesium is the element with the ordinal number 12, aluminum is number 13 and a very different material. "Baker's magnesium" actually has more applications in baking (namely, [foil]).
In the title text, 144 (12x12) is a gross. 169 (13x13) would be a baker's gross, an addition of not just one but 25 units.](https://cdn.masto.host/avgeeksocial/media_attachments/files/114/548/897/426/787/126/original/c23f71d0e38d4910.png "explanation from explainXKCD https://www.explainxkcd.com/wiki/index.php/3092:_Baker%27s_Units
(truncated to fit)
A baker's dozen is 13 units of bakery goods, as opposed to the normal dozen meaning 12. [...]
Randall proceeds to apply this principle to other things comprised of 12 units, some with bizarre results:
Imperial feet are 12 inches long; a baker's foot would be 13 inches.
Noon is 12:00 o'clock [...]; baker's noon would be 1 o'clock PM (\"thirteen hundred hours\").
Dodecahedrons have 12 faces (the shape that most d12s take the form of), baker's ones are tridecahedrons (which are not Platonic solids [...]), rendering dice-based games unbalanced.
Years have 12 months; a baker would celebrate New Year's Eve on January 31 [...].
Octaves are comprised of 12 half-steps. A baker’s octave would have 13 half-steps and cause problems in musical composition, [...]
Trial juries in the Anglo-Saxon law tradition consist of 12 peers. The baker’s jury has 13 peers. [...]
The Flag of Europe has 12 stars forming a circle (unlike in the US flag, the stars do not represent member states. The flag was first adopted by the Council of Europe in 1955, when it already had 13 members [...])
Magnesium is the element with the ordinal number 12, aluminum is number 13 and a very different material. \"Baker's magnesium\" actually has more applications in baking (namely, [foil]).
In the title text, 144 (12x12) is a gross. 169 (13x13) would be a baker's gross, an addition of not just one but 25 units.")
Math is not only about numbers but a new way of thinking in this article we discussed how to become a master at math
Will computers prove theorems? ~ Kevin Buzzard. https://youtu.be/LylJBfvVzyw #ITP #LeanProver #Math
Now this animation is available for the 1000 sequences decomposed on my website.
Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages https://decompwlj.com/
A little more work on axis sizing and controls.
decompwlj.comDecomposition into weight × level + jump - 3D graphs - 2D graphs - First 500 terms - Rémi EismannDecomposition into weight × level + jump with 3D graphs (WebGL three.js), 2D graphs and first 500 terms. This decomposition is an extension of the fundamental theorem of arithmetic and a new way to see the numbers. 1000 sequences decomposed (natural numbers, prime numbers, triangular numbers, composites...). Rémi Eismann
Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:
The natural numbers (A000027) https://decompwlj.com/3DgraphGen/Natural_numbers.html
What does it mean (to you) to understand a piece of mathematics?
I am starting a new series on the blog for inquiries in math. I posted the first one today:
https://www.fractalkitty.com/inquiries-week-1-circle-shading/
Fractal Kitty · Inquiries-Week 1: Circle ShadingThis is the first of a series of guided inquiries in math. If a document is preferred over a blog post, the pdf file is below:
Inquiries-Week 1_ Circle ShadingInquiries-Week 1_ Circle Shading.pdf622 KBdownload-circle
Introduction
When circles overlap they make lunes:
or lenses:
or other fun shapes:
Activity
Let's
In Bonn there is a stall with vintage and used books. For 5 Euros I just bought a #math text book from 1968 that contains a chapter on #AnalogComputer #mathematics and programming:
Preuve (géométrique) de la formule de l'aire d'un triangle quelconque.
Edit: in English: geometric proof of the formula giving the area of a triangle.
`Although the term "matrix" was introduced into mathematical literature by James Joseph Sylvester in 1850, the credit for founding the theory of matrices must be given to Arthur Cayley, since he published the first expository articles on the subject. ... Cayley's introductory paper in matrix theory was written in French and published in a German periodical [in 1855]`
Maths HistoryArthur Cayley - BiographyArthur Cayley's most important work was in developing the algebra of matrices and work in non-euclidean and n-dimensional geometry.
We've had some incredible results in our mathematical modeling program this year, The latest: A team of three of our high school students won the Mathematical Association of America award for their submission to the university-level Mathematical Contest in Modeling run by COMAP! They were one of 18 teams out of 12,000 worldwide to earn an "Outstanding" designation for their mathematical projection of Olympic medal counts for the 2028 games.
https://contest.comap.com/undergraduate/contests/mcm/contests/2025/results/index.html
contest.comap.comThe Mathematical Contest in Modeling
Had to step in and remediate two faulty questions on my son's #Geometry homework tonight. Note to the "Teachers Pay Teachers" worksheet author: A regular octagon does not have 4 lines of symmetry.
Note: Thanks to @danielmclaury for pointing out I should have specified that it was a regular octagon on the homework handout.