#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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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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Math education as an academic discipline ought to spend less effort thinking about how to teach math to children and more effort thinking about why to teach it to them at all if they're not interested.
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The Silencing of Research - by Jo Boaler https://thethreo.com/the-silencing-of-research/
#EdResearch #MathEducation #Education -
Math teachers used to require expensive graphing calculators because they had advanced capabilities. Now we require expensive graphing calculators because they can't run photomath. The calculators are still expensive, though, for no reason at all.
#Mathematics #MathEducation #Calculators #GraphingCalculators #Capitalism
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Math teachers used to require expensive graphing calculators because they had advanced capabilities. Now we require expensive graphing calculators because they can't run photomath. The calculators are still expensive, though, for no reason at all.
#Mathematics #MathEducation #Calculators #GraphingCalculators #Capitalism
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#SouthwestVirginia news in the #WashingtonPost is somewhat rare, as is good news about #MathEducation and teachers finding ways to compensate for the clobbering #math students, parents and teachers took from covid. Have a twofer! #Roanoke #MiddleSchool
#Virginia #VirginiaNews
https://www.washingtonpost.com/education/2022/12/30/middle-school-math-pandemic-recovery/?fb_news_token=CX0JftSNz23Mne3EM4q1vQ%3D%3D.Reos8mx7dSuan1qGUVW%2FuNBL4ZrSgUOk8wbryOoXJJQGRFStI2TsACgN8j7THwM%2FLZrMv41FMdGjh3J1STNW7%2F5Mhb%2B9994N5mRQvlKHoMItke6YxkSmAGFs07ALRIW0TX0dxcXF4cIv48fXp6y2F9%2F8huyxDrMy3XBBPQM0lisOBcJFnu64xFzMrlRHre8hLk2JvBVnQ%2Fzqnov6cdlicCNijcDIn95mUo02beofn8zZhng1Od5S74qX8Ftf3KM%2Bl%2Fq%2BpTZuGYtf2cRuQJPXvVIzsqSUHjmeqgxxAjg0f%2FamEifKCIfvYIgyYgLi%2FNNUxquCtp6VCA%2B4CD6XqkRAAJl8%2BlXjFD9dnKNPrbeHqQY%3D -
Stories of Algebra https://sites.google.com/view/stories-of-algebra
Students create & solve math problems related to their career interests (#SituatedLearning).
Candace Walkington et al. used the free ASSISTments platform for #FormativeAssessment & #AdaptiveLearning: https://new.assistments.org/
#ClosedAccess article just published: https://www.tandfonline.com/doi/abs/10.1080/0020739X.2022.2128458
Similar #OpenAccess article by the same authors: https://drive.google.com/file/d/1dw5aBadszlPrEV4uvZEDH1l0jK1WvWXU/view
#MathEducation -
Stories of Algebra https://sites.google.com/view/stories-of-algebra
Students create & solve math problems related to their career interests (#SituatedLearning).
Candace Walkington et al. used the free ASSISTments platform for #FormativeAssessment & #AdaptiveLearning: https://new.assistments.org/
#ClosedAccess article just published: https://www.tandfonline.com/doi/abs/10.1080/0020739X.2022.2128458
Similar #OpenAccess article by the same authors: https://drive.google.com/file/d/1dw5aBadszlPrEV4uvZEDH1l0jK1WvWXU/view
#MathEducation
