#matheducation — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #matheducation, aggregated by home.social.
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From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨
In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,
aᵖ ≡ a (mod p).
For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”
About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.
#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge
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From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨
In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,
aᵖ ≡ a (mod p).
For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”
About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.
#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge
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Frenet–Serret Formula ✍️
It explains how a curve reveals its hidden geometry by tracking the way it bends and twists through space. Imagine tracing the path of a roller coaster, a winding river, or the spiral of a DNA strand. At every point along the path, the curve is constantly changing direction, and the Frenet–Serret formulas provide a precise way to describe that change.
They do this by attaching a moving frame of three special directions to each point on the curve. The first points forward along the path, showing where the curve is heading. The second points inward, toward the direction of bending. The third stands perpendicular to both, capturing how the curve twists out of its plane. Together, they form a local coordinate system that travels with the curve itself.
As you move along the curve, these three directions rotate and evolve. The formulas measure this evolution using two key quantities: curvature and torsion. Curvature tells how sharply the path bends, while torsion tells how strongly it twists into three dimensions. If curvature vanishes, the path becomes straight; if torsion vanishes, the curve lies flat in a plane.
Mathematicians and physicists use the Frenet–Serret formulas to study motion, design smooth paths in engineering, understand particle trajectories, and analyze natural shapes. They transform a simple line into a rich geometric story, revealing exactly how space is being navigated at every step.
#FrenetSerretFormula #DifferentialGeometry #Geometry #Mathematics #Math #PureMathematics #AppliedMathematics #MathematicalPhysics #Physics #STEM #ScienceEducation #MathEducation #Curvature #Torsion #SpaceCurves #VectorCalculus #Calculus #LinearAlgebra #GeometricAnalysis
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Frenet–Serret Formula ✍️
It explains how a curve reveals its hidden geometry by tracking the way it bends and twists through space. Imagine tracing the path of a roller coaster, a winding river, or the spiral of a DNA strand. At every point along the path, the curve is constantly changing direction, and the Frenet–Serret formulas provide a precise way to describe that change.
They do this by attaching a moving frame of three special directions to each point on the curve. The first points forward along the path, showing where the curve is heading. The second points inward, toward the direction of bending. The third stands perpendicular to both, capturing how the curve twists out of its plane. Together, they form a local coordinate system that travels with the curve itself.
As you move along the curve, these three directions rotate and evolve. The formulas measure this evolution using two key quantities: curvature and torsion. Curvature tells how sharply the path bends, while torsion tells how strongly it twists into three dimensions. If curvature vanishes, the path becomes straight; if torsion vanishes, the curve lies flat in a plane.
Mathematicians and physicists use the Frenet–Serret formulas to study motion, design smooth paths in engineering, understand particle trajectories, and analyze natural shapes. They transform a simple line into a rich geometric story, revealing exactly how space is being navigated at every step.
#FrenetSerretFormula #DifferentialGeometry #Geometry #Mathematics #Math #PureMathematics #AppliedMathematics #MathematicalPhysics #Physics #STEM #ScienceEducation #MathEducation #Curvature #Torsion #SpaceCurves #VectorCalculus #Calculus #LinearAlgebra #GeometricAnalysis
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🔍 Oh, joy! Another 2017 gem where complex mathematical concepts are reduced to "three pictures"—because that's exactly how everyone comprehends Maxwell's equations, right? 🤯 Let's ignore the fact that differential geometry isn't really a bedtime story, but hey, who doesn't love a good abstract with a side of donation plea? 📚💸
https://arxiv.org/abs/1709.08492 #matheducation #complexconcepts #maxwells_equations #differentialgeometry #fundraising #HackerNews #ngated -
🔍 Oh, joy! Another 2017 gem where complex mathematical concepts are reduced to "three pictures"—because that's exactly how everyone comprehends Maxwell's equations, right? 🤯 Let's ignore the fact that differential geometry isn't really a bedtime story, but hey, who doesn't love a good abstract with a side of donation plea? 📚💸
https://arxiv.org/abs/1709.08492 #matheducation #complexconcepts #maxwells_equations #differentialgeometry #fundraising #HackerNews #ngated -
📣 Final lecture of the EMS Lecture Series on Mathematics Education (live)
🗓️ 12 Jun 2026 • 19:00 CEST • Online
🎙️ Terence Tao: How should students control their AI diet?
👤 Hosted by Tom Crawford
Abstract: “In an age where physical sustenance is plentiful, humans have to be mindful of their diet and exercise. With the advent of advanced AI tools that can provide intellectual sustenance, humans – and particularly students – will similarly need to manage their intellectual diet and exercise. I will share some of my own thoughts on these topics.”
▶️ Watch (live + replays): https://www.youtube.com/@EuropeanMathematicalSociety/streams
ℹ️ Series info & programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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📣 Final lecture of the EMS Lecture Series on Mathematics Education (live)
🗓️ 12 Jun 2026 • 19:00 CEST • Online
🎙️ Terence Tao: How should students control their AI diet?
👤 Hosted by Tom Crawford
Abstract: “In an age where physical sustenance is plentiful, humans have to be mindful of their diet and exercise. With the advent of advanced AI tools that can provide intellectual sustenance, humans – and particularly students – will similarly need to manage their intellectual diet and exercise. I will share some of my own thoughts on these topics.”
▶️ Watch (live + replays): https://www.youtube.com/@EuropeanMathematicalSociety/streams
ℹ️ Series info & programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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📣 EMS Lecture Series on Mathematics Education continues
🗓️ Friday, 10 April 2026 • 19:00 CEST • Online
🎙️ Sarah Powell: Supporting students with math difficulties
Focus on students who experience difficulty with mathematics: common areas of difficulty and five research-validated strategies to support learning.
👤 Hosted by Dr Tom Crawford.
▶️ Watch live on EMS YouTube: https://www.youtube.com/c/EuropeanMathematicalSociety/live
ℹ️ Series info & programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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📣 EMS Lecture Series on Mathematics Education continues
🗓️ Friday, 10 April 2026 • 19:00 CEST • Online
🎙️ Sarah Powell: Supporting students with math difficulties
Focus on students who experience difficulty with mathematics: common areas of difficulty and five research-validated strategies to support learning.
👤 Hosted by Dr Tom Crawford.
▶️ Watch live on EMS YouTube: https://www.youtube.com/c/EuropeanMathematicalSociety/live
ℹ️ Series info & programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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Ah yes, the noble quest of documenting every single prime number that can fit into a 32-bit integer. 🤓 A gripping tale that will leave readers at the edge of their seats as they discover the thrilling world of little-endian binary files. 🔍 Next time, try writing a novel to convey your incredible journey of reinventing a math teacher's weeknight lecture. 📜💤
https://hnlyman.github.io/pages/prime32_I.html #primeNumbers #littleEndian #binaryFiles #mathEducation #codingAdventure #HackerNews #ngated -
Ah yes, the noble quest of documenting every single prime number that can fit into a 32-bit integer. 🤓 A gripping tale that will leave readers at the edge of their seats as they discover the thrilling world of little-endian binary files. 🔍 Next time, try writing a novel to convey your incredible journey of reinventing a math teacher's weeknight lecture. 📜💤
https://hnlyman.github.io/pages/prime32_I.html #primeNumbers #littleEndian #binaryFiles #mathEducation #codingAdventure #HackerNews #ngated -
Math Teaching: Student Support and My Teaching Journey #matheducation #teacherlife… https://ift.tt/Zs1DYOz
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📣 The EMS Lecture Series on Mathematics Education continues in 2 weeks!
🗓️ Fri 13 February 2026 • 19:00 CET • Online
🎙️ Nuno Crato & Tim Surma: Improving mathematical learning with principles of human cognition
▶️ Live: https://www.youtube.com/@EuropeanMathematicalSociety/streams
ℹ️ Programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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📣 The EMS Lecture Series on Mathematics Education continues in 2 weeks!
🗓️ Fri 13 February 2026 • 19:00 CET • Online
🎙️ Nuno Crato & Tim Surma: Improving mathematical learning with principles of human cognition
▶️ Live: https://www.youtube.com/@EuropeanMathematicalSociety/streams
ℹ️ Programme: https://euromathsoc.org/news/ems-lecture-series-on-mathematics-education-190
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Is this geometry problem fun or is it evil?
“prove LMNO is a parallelogram” #matheducation -
Is this geometry problem fun or is it evil?
“prove LMNO is a parallelogram” #matheducation -
🥤🤔 Ah, yes, the Fourier Transform: because who wouldn't want to compare calculus to making smoothies? 🍓🔍 Apparently, dense equations are out, and your blender is the new math professor. 📚✌️
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ #FourierTransform #SmoothieMath #CalculusFun #MathEducation #BlenderScience #HackerNews #ngated -
🥤🤔 Ah, yes, the Fourier Transform: because who wouldn't want to compare calculus to making smoothies? 🍓🔍 Apparently, dense equations are out, and your blender is the new math professor. 📚✌️
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/ #FourierTransform #SmoothieMath #CalculusFun #MathEducation #BlenderScience #HackerNews #ngated -
An Interactive Guide to the Fourier Transform
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
#HackerNews #FourierTransform #InteractiveGuide #MathEducation #SignalProcessing
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An Interactive Guide to the Fourier Transform
https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
#HackerNews #FourierTransform #InteractiveGuide #MathEducation #SignalProcessing
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Here is a “magic trick”
Give kids colored cards.
red card- 1 dot
blue card- 2 dots
green card- 4 dots
yellow card- 8 dots“Show me a total of x dots!”
(x is a number between 1 and 15)“look around, why are you all holding up the same cards? isn’t anyone creative enough to find another way?”
then ask what goes on the “next card” #matheducation #math #binary
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Here is a “magic trick”
Give kids colored cards.
red card- 1 dot
blue card- 2 dots
green card- 4 dots
yellow card- 8 dots“Show me a total of x dots!”
(x is a number between 1 and 15)“look around, why are you all holding up the same cards? isn’t anyone creative enough to find another way?”
then ask what goes on the “next card” #matheducation #math #binary
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The TI-34 is a fairly basic scientific #calculator. I’m a big fan because it’s easy to use and not overwhelming.
I was reading the manual and discovered it has two functions:
ipart(x)
fpart(x)These return the integer and fraction parts of x.
ipart(2.34)=2
fpart(2.34)=.34Great! So, uh.. What are these typically used for? Why include them on such a *basic* calculator? #calculators #ticalc #ti34 #matheducation #mathchat
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The TI-34 is a fairly basic scientific #calculator. I’m a big fan because it’s easy to use and not overwhelming.
I was reading the manual and discovered it has two functions:
ipart(x)
fpart(x)These return the integer and fraction parts of x.
ipart(2.34)=2
fpart(2.34)=.34Great! So, uh.. What are these typically used for? Why include them on such a *basic* calculator? #calculators #ticalc #ti34 #matheducation #mathchat
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Just a life update:
I had been looking at ways to be finally licensed to teach, and I think I finally found it.
I actually got in touch with someone at SJ state, mapped out courses, got the confirmation that I do need to take the CSET test 1 but now I know I don’t have to take 2 and 3.
Also I took a practice test today and I had forgotten to take my meds. I only realized it when I simply couldn’t concentrate enough to finish a problem half way through. The change was so obvious once I took them that it really saddened me to think about unmedicated folks struggling. No wonder I couldn’t pass the praxis 6 times!
This experience today made me think of I want to do beyond getting my license. The idea i got is to work on a curriculum that also incorporates the whole ADHD person. It’ll have pauses in between problems. It’ll force you to take breaks if you become intensely focused like I got (it became OCD which I was treated for) or to get up / fidget if you need to. It’ll also have short snippets on math anxiety, growth mindset, how adhd affects your working memory and evidence based tips that can help with that.
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Just a life update:
I had been looking at ways to be finally licensed to teach, and I think I finally found it.
I actually got in touch with someone at SJ state, mapped out courses, got the confirmation that I do need to take the CSET test 1 but now I know I don’t have to take 2 and 3.
Also I took a practice test today and I had forgotten to take my meds. I only realized it when I simply couldn’t concentrate enough to finish a problem half way through. The change was so obvious once I took them that it really saddened me to think about unmedicated folks struggling. No wonder I couldn’t pass the praxis 6 times!
This experience today made me think of I want to do beyond getting my license. The idea i got is to work on a curriculum that also incorporates the whole ADHD person. It’ll have pauses in between problems. It’ll force you to take breaks if you become intensely focused like I got (it became OCD which I was treated for) or to get up / fidget if you need to. It’ll also have short snippets on math anxiety, growth mindset, how adhd affects your working memory and evidence based tips that can help with that.
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Function Notation: My Favorite Lesson Taught Again! #MathEducation #Algebra… https://ift.tt/DBvwQGq
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An Illustrated Introduction to Linear Algebra, Chapter 2: The Dot Product
https://www.ducktyped.org/p/linear-algebra-chapter-2-the-dot
#HackerNews #LinearAlgebra #DotProduct #IllustratedIntroduction #MathEducation #DataScience
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An Illustrated Introduction to Linear Algebra, Chapter 2: The Dot Product
https://www.ducktyped.org/p/linear-algebra-chapter-2-the-dot
#HackerNews #LinearAlgebra #DotProduct #IllustratedIntroduction #MathEducation #DataScience
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Have any math teachers on here used minecraft (eg arrows to teach about parabolas. You can use command blocks to make the parabolas physical arcs when you fire. Or redstone for logic?)
There is also something called "educational minecraft" apparently.
Thought I might mess around with it this summer, but don't know if it's worth the time or if I'm just making up an excuse for me to play video games. (very possible)
Curious what it was like *in a class*
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Have any math teachers on here used minecraft (eg arrows to teach about parabolas. You can use command blocks to make the parabolas physical arcs when you fire. Or redstone for logic?)
There is also something called "educational minecraft" apparently.
Thought I might mess around with it this summer, but don't know if it's worth the time or if I'm just making up an excuse for me to play video games. (very possible)
Curious what it was like *in a class*
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"🤓 Let's dive into the thrilling world of the Peano Axioms—you know, those edge-of-your-seat, pulse-pounding rules that define 1, 2, and 3 like it's rocket science 🚀. Because who needs action movies when you can have 'Axiomatic Studies' instead? 📚💤"
https://principlesofcryptography.com/number-theory-primer-an-axiomatic-study-of-natural-numbers-peano-axioms/ #PeanoAxioms #MathEducation #AxiomaticStudies #LogicNerds #MathIsFun #HackerNews #ngated -
"🤓 Let's dive into the thrilling world of the Peano Axioms—you know, those edge-of-your-seat, pulse-pounding rules that define 1, 2, and 3 like it's rocket science 🚀. Because who needs action movies when you can have 'Axiomatic Studies' instead? 📚💤"
https://principlesofcryptography.com/number-theory-primer-an-axiomatic-study-of-natural-numbers-peano-axioms/ #PeanoAxioms #MathEducation #AxiomaticStudies #LogicNerds #MathIsFun #HackerNews #ngated -
Differential Geometry: A First Course in Curves and Surfaces [pdf]
https://math.franklin.uga.edu/sites/default/files/users/user317/ShifrinDiffGeo.pdf
#HackerNews #DifferentialGeometry #Curves #Surfaces #MathEducation #PDF #Resources
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Differential Geometry: A First Course in Curves and Surfaces [pdf]
https://math.franklin.uga.edu/sites/default/files/users/user317/ShifrinDiffGeo.pdf
#HackerNews #DifferentialGeometry #Curves #Surfaces #MathEducation #PDF #Resources
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I've spent today making a poster for Newcastle Uni's teaching and learning conference.
I started off making it in Inkscape but quickly got fed up with laying out text, so switched to a web page. I'm quite happy with how it turned out!
And as a bonus, I automatically get a digital version I can direct people to with a QR code.
Online at https://improving-accessibility-ltconf-2025.think.somethingorotherwhatever.com
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I've spent today making a poster for Newcastle Uni's teaching and learning conference.
I started off making it in Inkscape but quickly got fed up with laying out text, so switched to a web page. I'm quite happy with how it turned out!
And as a bonus, I automatically get a digital version I can direct people to with a QR code.
Online at https://improving-accessibility-ltconf-2025.think.somethingorotherwhatever.com