#appliedmathematics — Public Fediverse posts

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

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

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

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

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

💼 #Job #opportunities

3 x #ResearchFellow roles to work on #ESRCfunded Connecting #Generations projects, based at the #UniversityofStAndrews

📨 Apply by 29 June. More info: https://www.cpc.ac.uk/news/vacancies/

#jobs #researchjobs #jobsearch #demography #statistics #computerscience #appliedmathematics #phd #Geography #socialscience #longitudinaldata #dataanalysis #qualitativedata #eventhistoryanalysis #population #intergenerational #family #fertility #socialsciences #migration #community

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

My #introduction keywords: #academic #modelling #evolution #cooperation #gameTheory #ecology #appliedMathematics

I'm a #postdoc specialising in evolutionary and ecological modelling, currently at #QUT and #GriffithsUni in #Australia

Previous work: #evolutionOfCooperation, estimating undetected #extinctions, #qualitativemodelling, migratory #phenology, #foodweb #modelling, local #adaptation, #carryover effects, #dispersal.

My blog: https://nadiah.org/

“My PhD was all about understanding what happens to blood flow in collapsible blood vessels like the giraffe jugular vein. In my postdoc I was investigating how to optimise ventilator settings for patients in ICU and then how to deliver inhaled therapies into the lungs. Since then, my focus has been in trying to understand how diseases like Asthma and other respiratory diseases originate and then progress. This involves incorporating biology and physics into mathematical and computational models, using approaches from different areas of applied maths. More recently I have started to look into the mechanisms that could lead to a rare lung disease called lymphangioleiomyomatosis (LAM) and Long Covid.” - Bindi Brook

➡️ https://hermathsstory.eu/bindi-brook/

#Academia #PhD #Professor #AppliedMathematics #MathematicalBiology #MathematicalMedicine #UnconsciousBias #WomenInMaths #WomenInSTEM #HerMathsStory

“Since my goal was to solve a problem no one had ever solved before, it required a creative and flexible approach, one that emphasized the exploration, experimentation, and steady refinement of ideas. But perhaps the most important lesson I learned was that there is no single “correct” way to be a mathematician.” - Katy Micek

➡️ Find the full story at https://hermathsstory.eu/catherine-micek/

#PhD #WomenInMaths #WomenInSTEM #HerMathsStory #AppliedMathematics #DataScience #MachineLearning

"The realization that mathematical concepts and theory could directly impact and improve real-world problems...fueled my passion for pursuing further research and applications that bridge theory with practice" - Anna Ma

➡️ https://hermathsstory.eu/anna-ma/

#Academia #AppliedMathematics #WomenInMaths #WomenInSTEM #HerMathsStory

“(...) My students have used their knowledge to model the oil spill in the Gulf of Mexico, analyze income inequality in New York City using the Gini coefficient, and determine appropriate drug dosages, among other projects. These projects not only deepen their understanding of mathematical concepts but also highlight how mathematics can be a powerful tool for analyzing and solving real-world problems. By exploring the intersection of social justice and mathematics, students gain a broader perspective on how their skills can contribute to meaningful change in society.” - Mónica D. Morales-Hernández

➡️ https://hermathsstory.eu/monica-d-morales-hernandez/

#Academia #AssistantTeachingProfessor #Educator #AppliedMathematics #ComputationalMathematics #Physics #SocialJustice #Classism #Sexism #Racism #Volunteering #WomenInMaths #WomenInSTEM #LatinaInSTEM #HerMathsStory