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Source code of Mathigon's interactive textbooks
Home Page: https://mathigon.org
textbooks's Introduction
Mathigon Textbooks
Welcome to Mathigon, an award-winning mathematics education platform for students aged 12 to 18. Part textbook and part virtual personal tutor, it uses cutting-edge technology and an innovative new curriculum to make learning mathematics more fun and more interactive and engaging than ever before. Learn more…
This repository contains the source code and assets for all our courses.
Setup
If you want to make changes or additions to this content, you can run a local Node.js server for development. First, make sure you have NPM and Node.js (version 14+) installed on your computer, or download them from the official page.
Next, clone this repository, install all dependencies, and then start a local server using these commands:
git clone https://github.com/mathigon/textbooks cd textbooks npm install npm start Running npm start for the first time may take a few minutes, as it compiles all existing courses. Later, it should use cached versions whenever possible. Finally, you can visit localhost:5000 and select any of the chapters.
The server will watch for changes to any of the files and recompile automatically whenever necessary (with a few exceptions like shared or YAML files).
Contributing
We welcome any contributions to Mathigon – from bug fixes and correcting typos to creating entirely new courses. If you find any bugs or mistakes, please file an issue.
When writing new content, make sure you follow our content development guide, which contains pedagogical principles, style recommendations, and descriptions of interactive elements.
If you want to help us translate Mathigon into more languages, take a look at our localisation documentation.
Before submitting a pull request, you have to sign our Individual Contributor License Agreement.
If you want to work for Mathigon, visit our careers page, and contact us if you have any questions.
Documentation
Course Structure
Every course is a subfolder in the content directory, and consists of these components:
-
content.mdcontains the source code and metadata for a course. It is written in a custom extension of Markdown. More documentation… -
functions.tscontains all the TypeScript code for all the interactive elements in this course. More documentation… -
styles.scsscontains all course-specific styles, written in SCSS. -
hints.yaml(optional) contains any messages that can be sent by Mathigon's virtual tutor.
The content/shared directory contains biographies, glossary, web components, and assets used by multiple courses.
Dependencies
This repository contains all the code and content for our interactive courses. Its dependencies include a number of separate libraries that are published on NPM. In most cases, you should not have to make changes to these libraries directly, but it may be helpful to look at their documentation:
- @mathigon/core contains JavaScript utilities such as array and string manipulation, promises, function caching, and event handling.
- @mathigon/fermat is a powerful mathematics library for TypeScript. It contains everything from number theory to random numbers and linear algebra classes.
- @mathigon/hilbert handles expression parsing, simplification, and MathML rendering.
- @mathigon/euclid contains Geometry classes as well as SVG and Canvas drawing utilities.
- @mathigon/boost contains browser utilities such as DOM selections, web components, gesture recognisers, animations, routing, multi-threading and AJAX requests.
- @mathigon/studio contains the base NodeJS server, TypeScript components and markdown parser for our interactive courses.
Testing and Linting
Before submitting a pull request, make sure to run npm run lint-fix, to ensure a consistent coding style across all files.
TODO: Unit and screendiff tests
Translations and Localisation
Translations are powered by GitLocalize. In order to help us translate content, you have to create a GitHub account and then contact us to be added to the list of editors. This blog post explains how you can use the GitLocalize platform to add new languages, translate new courses, or fix bugs in existing translations.
Audio Narrations
To generate audio narration files for the text in all courses, using the Google Cloud TTS API, you first need to install FFmpeg, for example using brew install ffmpeg. Then simply run node utilities/audio.js.
© Mathigon 2016–2021, All rights reserved
textbooks's Issues
Complete the Nets and Cross Sections section in "Polygons and Polyhedra"
Directed graph glossary
I am working on the french translation of the glossary.
In a directed graph, every edge as an arrow, i.e. a start vertex and an end vertex.
Is it a correct english sentence ? I understand the meaning of the sentence (so I can translate it) but it doesn't seems correct in english. However I might be wrong as english is not my main language.
Interactive: Prisoners' Paradox
An interactive game, where students can play the prisoners' paradox against another player, or the computer.
Similar to https://youtu.be/_q4DrUHKC0Q?t=2230
TBD: how to select other users, e.g. can two students play on the same device simultaneously, do we link with other students logged into the same class on Mathigon, or random users from the web?
Fix handshake table on Mobile
The handshake table in Graphs and Networks is broken on mobile devices:
Don't rescale coordinate system axis in Sequences course
We shouldn't rescale the y-axis in these coordinate systems, so that students get a better idea of how the variable parameters affect the growth of the sequence:
https://mathigon.org/course/sequences/arithmetic-geometric#arithmetic-geometric-graph
Typo in timeline
Claude Shannon's lifetime is (1916 - 2001) according to Wikipedia. But in timeline activity of Mathigon, both on website and Android app it mentions (1898 – 1972).
minor typo in glossary.yaml [ polyhedron ]
polyhedron:
title: Polyhedron
text: A polyhedron (the plural is polyhedra) is a 3-dimensional solid
with no curves surfaces or edges. All faces of a polyhedron are polygons.
For example, a cube and a pyramid are polyhedra, but a sphere is not.
link: /course/polyhedra/polyhedra
should read as follows:
polyhedron:
title: Polyhedron
text: A polyhedron (the plural is polyhedra) is a 3-dimensional solid
with no curved surfaces or edges. All faces of a polyhedron are polygons.
For example, a cube and a pyramid are polyhedra, but a sphere is not.
link: /course/polyhedra/polyhedra
Add Graph Drawing Interactive in "Graphs and Networks"
Allow students to make their own graphs, and try to draw them with a single stroke
Translated versions of Pythagoras' Theorem shown as empty pages
When I change the language on the Pythagoras' Theorem textbook eg. to german, the already translated page doesn't show up.
Gulp doesn't watch .pug files for changes
I was trying to customize the content/transformations/components/wallpaper.pug file, but noticed that Gulp doesn't watch files with .pug extension for changes to auto-run the parser and renderer. Here's the Gulp config: https://github.com/mathigon/textbooks/blob/master/gulpfile.js#L49-L53
This would be useful to have. Currently, I need to run rm content/.cache.json && npm start after every change in these .pug files.
Completion of exercise on Congruence is not detected
In the course on Euclid's Axioms, the section on Congruence does not automatically display the next batch of text after the exercises is completed, which looks like a bug.
The workaround is for the user to click on the message "Are you stuck? Skip to the next step or reveal all steps"
Action Required: Fix Renovate Configuration
There is an error with this repository's Renovate configuration that needs to be fixed. As a precaution, Renovate will stop PRs until it is resolved.
Error type: undefined. Note: this is a nested preset so please contact the preset author if you are unable to fix it yourself.
Add rotating arc for plant growing interactive (Sequences)
This interactive diagram shows how the angle between consecutive leaves in a plant is always constant. We should add a rotating arc that visualises this:
https://mathigon.org/course/sequences/fibonacci#sunflower-growing
Dependency Dashboard
This issue provides visibility into Renovate updates and their statuses. Learn more
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- Update Tests (
@typescript-eslint/eslint-plugin,@typescript-eslint/parser,eslint,eslint-plugin-import) - Update dependency typescript to v4.5.2
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These updates are pending. To force PRs open, click the checkbox below.
- Update dependency css-what to 5.0.1 [SECURITY]
- Update dependency nth-check to 2.0.1 [SECURITY]
- Update dependency path-parse to 1.0.7 [SECURITY]
- Check this box to trigger a request for Renovate to run again on this repository
Translation and country specificity
(Just some though, I don't plan to translate those course for the moment)
-
In France, we start our sequence at rank 0 (which simplify a lots of formula !).
When translating, should the translater rewrite the course so that sequence start at rank 0 to follow french way to do ? What about Canada (which also have french as main language), I checked really quick but it seems that they start their sequence at rank 1. I think french course should follow France guideline and start at rank 0. -
In France, in reccurcive formula, we usually give u(n+1) in function of u(n) instead of giving u(n) in function of u(n-1). What should the translator do ? I Think u(n) in function of u(n-1) is easier to understand, but it would then means that student have different reccursive formula than formula at their school (which shouldn't be a problem if they really understand what the formula means but this might still bug lots of students).
-
More problematic, we (but France is pronanly not be the only country to do that) also have a totally different definition for limit. We say that « f tends to L as x tends to a if for every ɛ>0 there exists δ>0 such that for every x in the domain of f, |x - a| ≤ δ implies that |f(x) - L| ≤ ɛ » while your definition also require that 0 < | x - a |. So some function might have limit with english definition but not with french definition. Again, what the translator should do ?
I repeat, it's just some though, I don't plan to translate those course for the moment.
Shift rectangles when demonstrating quadrilateral area
In Polygons and Polyhedra, users are asked to draw rectangles with the same size as given parallelograms or trapeziums. The area check works correctly, but we should shift user's rectangles if they don't correspond to the the position assumed in the explanation:
I do not understand `$step.model.*`
Codes:
$step . model . rad = ( r: number ) => { const a = r / Math . PI ; return a > 1.99 ? 2 : round ( a , 2 ) ; } ; const zero = new Point ( 240 , 140 ) ; const center = new Point ( 140 , 140 ) ; const ends = [ new Point ( 240 , 140.4 ) , new Point ( 40 , 140 ) , new Point ( 140 , 40 ) ] ; function setState ( i: number ) { const arc1 = new Angle ( $step . model . a , center , zero ) . arc ; const arc2 = new Angle ( $step . model . b , center , ends [ i ] ) . arc ; animate ( ( p ) => { $step . model . a = arc1 . at ( p ) ; $step . model . b = arc2 . at ( p ) ; } , 600 ) ; }
How do I understand $step.model.rad, $step.model.a and $step.model.b ?
When I try write that:
import { SVGParentView , observe } from '@mathigon/boost' ; const $svg = new SVGParentView ( document . getElementById ( 'svg' ) ) ; console . log ( $svg . model ) ; $svg . bindModel ( observe ( $svg . $ ( '.a' ) ) ) ; $svg . bindModel ( observe ( $svg . $ ( '.b' ) ) ) ; console . log ( $svg . model ) ; // => Only one
So what can I bind model for myself?
machine translation should be indicated
I believe that machine translation should be used with caution in the texts on mathematical topics, because mathematical terms are rarely used correctly. At least in the German translation, they may cause more harm than good to the pupils and students.
Therefore it would be absolutely necessary to mark these translations as machine translations which should be used with caution.
Interactive: Galton Board
Create an interactive Galton board, where small balls fall down a grid of pegs to form an approximately normal distribution:
Students should have a slider to offset the center of the pegs, to create skewed distributions.
Prevent cheating in Königsberg Bridges
For the Königsberg Bridges problem in Graphs and Networks, you can cheat by moving the cursor outside the city area:
Interactive: Virtual Enigma
A virtual enigma machine: students can click keys on a keyboard, at which point the corresponding cipher letter lights up, and the rotors move by one. Students can also switch out different rotors, or connect differently plugs on the plugboard.
Similar to this, but with nicer graphics?
After creating a ciphertext, students should be able to send it to a friend (together with initial setup instructions), who should then be able to decipher it using the same component.
Interactive: Logistic Map
An interactive simulation that shows how to generate the logistic map.
References:
https://www.youtube.com/watch?v=ovJcsL7vyrk
https://geoffboeing.com/2015/03/chaos-theory-logistic-map/
This should consist of a series of different elements:
- Two side-by-side coordinate systems, one showing the convergence, and one tracking the value of the equilibrium positions, as students move a slider that changes the value of lambda.
-
A high-res version of the logistic map, that allows students to zoom in
-
(bonus) A 3D version that illustrates its relation to the Mandelbrot set.
Some idea for a "logic" chapter for young student
Hi,
There is currently a logic chapter on mathigon but it's more aimed to advanced student.
I wrote the last years an article for a blog I have at my school. It is aimed on giving some basics notion on logic. It is a little fun and verry accessible.
I post it here because it might give some idea if you ever want to write a logic chapter for not advanced student.
Unfortunatly it's in french.
https://mathematiques.xyz/blog/Logique/article.html
Ps : The article it's in C0 but picture are not because I didn't make them (they are CC-BY though)
Interactive: Ellipse drawing
An interactive component for the Conic Sections course, that allows students to draw an ellipse using a virtual pencil and a rope that is connected to two pegs (the foci of the ellipse):
Students should be able to move the pencil as well as the position of the two foci, by clicking and dragging with finger or mouse.
The rope needs some basic physics simulation (rope/chain) to model behaviour when it is slack. The pencil should be movable to anywhere within the ellipse, not just the positions along the edge, and leave a faint trail of where it has been.
Lowest Common Multiple race - Add a starting line
<rect x= "378" width= "4" height= "88.2" y= "177.6" fill= "white" ></rect>
or
<rect x= "370" width= "9.8" height= "9.8" y= "177.6" fill= "black" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "177.6" fill= "white" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "187.4" fill= "white" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "187.4" fill= "black" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "197.2" fill= "black" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "197.2" fill= "white" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "207.0" fill= "white" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "207.0" fill= "black" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "216.8" fill= "black" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "216.8" fill= "white" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "226.6" fill= "white" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "226.6" fill= "black" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "236.4" fill= "black" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "236.4" fill= "white" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "246.2" fill= "white" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "246.2" fill= "black" ></rect> <rect x= "370" width= "9.8" height= "9.8" y= "256.0" fill= "black" ></rect><rect x= "380" width= "9.8" height= "9.8" y= "256.0" fill= "white" ></rect>
I think the first one is better.
Improve WebGL Polyhedra
- Better interactive rotations
- Momentum and damping
- Automatic rotations on Firefox and Safari
Slow down the Sieve of Eratosthenes animations (Sequences)
We should slow down the colour animations in the Sieve of Eratosthenes grid, so that it's easier to see what's going on:
https://mathigon.org/course/sequences/special#primes-2
Complete the Composition section in "Transformations and Symmetry"
Cool video: https://www.youtube.com/watch?v=8NmHZEKkkpM
Interactive: Parabolic Mirror
An interactive, parabolic mirror, that shows how light from a fixed point is reflected in parallel rays. students can slide the position of the light bulb (to find the focus), and change the shape of the parabola (using a slider).
Bonus: Rather than having static lines to represent light rays, have a subtle animation (e.g. small arrows or beads slowly flowing along the ray, in the direction of the light).
Bonus 2: A few other types of shapes (e.g. semicircle), to show that slight rays are reflected differently.
Bonus 3: Swap the graphics to show how to heat an egg on a parabolic grill, using incoming light from the sun, or concentrate radio waves onto a detector in a radio telescope.
Complete Constructions in "Triangles and Trigonometry"
See https://mathigon.org/course/triangles-and-trigonometry#contruction
Improved Tessellation Builder
Improve the tessellation builder in Polygons and Polyhedra:
- Prevent overlapping, rather than simply highlighting it. (Use a physics engine?)
- Hide the rotate handles when users aren't hovering
- Fix intersection detection for rotated triangles and pentagons
- More intuitive moving/rotating on mobile
- Allow exporting to PNG
- Save user's progress to Mathigon's DB
Jade or Markdown?
Sum of quadrilateral angles should always be 360°
At the beginning of Polygons and Polyhedra, rounding errors can mean that the four angles in the quadrilateral don't actually add up to 360°. We should probably set the last angle to 360° – rounded other angles.
It is also possible to turn the quadrilateral "inside out":
Complete Isosceles+Equilateral and Trigonometry in "Triangles and Trigonometry"
See https://mathigon.org/course/triangles-and-trigonometry#isosceles
Add Recurrence Relation slider in sequences chapter
For many of the sequences, e.g.
https://mathigon.org/course/sequences/fibonacci#rabbits-3
it would be cool to ad an interactive "recurrence relation slider", as described here:
http://www.antonellaperucca.net/perucca-recurrence.pdf
Fix Ulam Spiral diagram on mobile
See https://mathigon.org/course/divisibility-and-primes#ulam
The diagram is currently broken on mobile:
vs
It doesn't consider all possible rectangles
In Polygons and Polyhedra, it asks to draw a rectangle with the same area. But it doesn't consider all possible rectangles.
- It rejects other dimensions other than 8 x 6. For example, it rejects 6 x 8, 4 x 12 and 12 x 4
- And also it rejects the rectangles that been drawn not staring from the left-top corner.
Add step to install Node in the Getting Started at the README file
Getting Started section in the README file does not contain any reference to the must-have requirement of having Node installed before running npm install command. This issue may present challenges to new contributors.
A reference to Node installation could be added as part of the Getting Started section in the README file as the first instruction as a check mark before proceeding with forking and cloning.
Complete the Geometry Construction section in "Euclidean geometry"
Add a license to the GitHub repository
Hi, Would it be possible for you to add a LICENSE file to the GitHub repository, e.g. with the text of the MIT or Apache 2 license (or whatever license you choose, of course)? This makes it easier for employees at companies such as Google to sign the CLA and contribute.
Prime checker display html tag
https://mathigon.org/course/divisibility/distribution-of-primes
Suggestion for fractal textbook
In the Mandelbrot set section of fractal textbook it is written that
In some cases, the sequence doesn't converge to a single point – instead it reaches a cycle of multiple points, like a triangle. These cycles are called orbits.
Many textbooks on dynamical systems call these cycles as periodic orbits, and the term orbit is used to refer to any trajectory of the dynamical system. Should not be better to change 'orbits' to 'periodic orbits'?
Interactive: Quadratics Angry Birds
An Angry Birds-style game, that shows how projectiles follow a parabolic path.
Preview: https://mathigon.org/course/quadratics/projectiles?preview
https://github.com/mathigon/textbooks/blob/master/content/quadratics/components/projectile.ts
Students have a slingshot at position (0, 0) and have to hit specific targets at other positions (fish?). You should be able to hide or show a coordinate system overlay.
The game should be a configurable custom webcomponent that can be used in two different settings:
- An exploratory version, where students drag a slingshot and can experiment with different angles and initial velocities.
- A static version where students have to calculate the equation for the required parabola that goes through two points. Upon finding the correct equation, play the slingshot animation.
Update THREE.js to the latest version
This will require replacing all uses of THREE.Geometry with THREE.BufferGemetry…
Complete Travelling Salesman Interactives in "Graphs and Networks"
See https://mathigon.org/course/graphs-and-networks#salesman
- Hamiltonian cycle diagrams
- Travelling Salesman Map Diagram
- Greedy and 2-opt algorithm animation
- Ant colony animation
A few more typos in the glossary
sieve-eratosthenes:
title: Sieve of Eratosthenes
text: The Sieve of Eratosthenes is a procedure for finding prime numbers,
by continuoulsy eliminating numbers that are not prime.
link: /course/divisibility/primes#eratosthenes
should read as follows:
sieve-eratosthenes:
title: Sieve of Eratosthenes
text: The Sieve of Eratosthenes is a procedure for finding prime numbers,
by continuously eliminating numbers that are not prime.
link: /course/divisibility/primes#eratosthenes
venn-diagram:
title: Venn Diagram
text: A __venn diagram__ visualises multiple properties or events that
overlap.
image: venn.svg
should read as follows:
venn-diagram:
title: Venn Diagram
text: A __Venn diagram__ visualises multiple properties or events that
overlap.
image: venn.svg
Sorry for not including these in the other issue that has been fixed.
Complete the Similarity section in Transformations and Symmetry
(see https://github.com/mathigon/textbooks/blob/master/content/transformations-and-symmetry/content.md)
typos in bios.yaml
al-haytham:
born: 965
died: 1050
name: Al-Haytham
bio: |
Hasan Ibn al-Haytham (أبو علي، الحسن بن الحسن بن الهيثم, c. 965 – 1050)
lived in Cairo during the Islamic Golden Age, and studied mathematics,
physics, astronomy, philosophy and medicine. He was a proponent of the
scientific method: the belief that any a scientific hypothesis must be
verified using experiments or mathematical logic – centuries before
European scientists during the Renaissance. ...
should read as follows:
al-haytham:
born: 965
died: 1050
name: Al-Haytham
bio: |
Hasan Ibn al-Haytham (أبو علي، الحسن بن الحسن بن الهيثم, c. 965 – 1050)
lived in Cairo during the Islamic Golden Age, and studied mathematics,
physics, astronomy, philosophy , and medicine. He was a proponent of the
scientific method: the belief that any a scientific hypothesis must be
verified using experiments or mathematical logic – centuries before
European scientists during the Renaissance.
al-karaji:
born: 953
died: 1029
name: Al-Karaji
bio: Muhammad Al-Karaji (ابو بکر محمد بن الحسن الکرجی, c. 953 – 1029) was
a Persian mathematician and engineer. He was the first person to use prove
by induction, which allowed him to prove the binomial theorem.
links:
- title: Proof by Induction
url: /world/Axioms_and_Proof
Should read as follows:
al-karaji:
born: 953
died: 1029
name: Al-Karaji
bio: Muhammad Al-Karaji (ابو بکر محمد بن الحسن الکرجی, c. 953 – 1029) was
a Persian mathematician and engineer. He was the first person to use proof
by induction, which allowed him to prove the binomial theorem.
links:
- title: Proof by Induction
url: /world/Axioms_and_Proof
al-khwarizmi:
born: 780
died: 850
name: Al-Khwarizmi
overflow: true
bio: |
The Persian mathematician Muhammad Al-Khwarizmi (محمد بن موسى الخوارزمي,
780 – 850) lived during the golden age of the Muslim Abbasid regime in
Baghdad. He worked at the "House of Wisdom", which contained the first large
collection of academic books since the destruction of the Library of
Alexandria.
Al-Khwarizmi has been called the "**father** of algebra" – in fact, the word Should read as follows:
al-khwarizmi:
born: 780
died: 850
name: Al-Khwarizmi
overflow: true
bio: |
The Persian mathematician Muhammad Al-Khwarizmi (محمد بن موسى الخوارزمي,
780 – 850) lived during the golden age of the Muslim Abbasid regime in
Baghdad. He worked at the "House of Wisdom", which contained the first large
collection of academic books since the destruction of the Library of
Alexandria.
Al-Khwarizmi has been called the "**Father** of algebra" – in fact, the word **This one comes up a lot. "Father of ....". In some cases, "Father is capitalized. IN other cases, it without quotes. Not sure if you want to standardize on a style.
It comes up with:**
- Al-Khwarizmi
- Aristotle
- Babbage
- Democritus
- Desargues
- Descartes
- Euclid
- Galileo
- Monge
- Shannon
- Turing
Other typos:
cardano:
born: 1501
died: 1576
name: Cardano
bio: |
The Italian Gerolamo Cardano (1501 – 1576) was one of the most
influential mathematicians and scientists of the Renaissance. He
investigated hypocycloids, published Tartaglia's and Ferrari's solution for
cubic and quartic equations, was the first European to systematically use
negative numbers, and even acknowledged the existing of imaginary numbers
(based on sqrt(-1)).
Cardano also made some early progress in probability theory and introduced binomial coefficients and binomial theorem to Europe. He invented many mechanical devices, including combination locks, gyroscopes with three degrees of freedom, and drive shafts (or Cardan shafts) that are still used in vehicles today. links:
- title: Imaginary Numbers
url: /world/Real_Irrational_Imaginary
Should read as follows:
cardano:
born: 1501
died: 1576
name: Cardano
bio: |
The Italian Gerolamo Cardano (1501 – 1576) was one of the most
influential mathematicians and scientists of the Renaissance. He
investigated hypercycloids, published Tartaglia's and Ferrari's solution for
cubic and quartic equations, was the first European to systematically use
negative numbers, and even acknowledged the existence of imaginary numbers
(based on sqrt(-1)).
Cardano also made some early progress in probability theory and introduced binomial coefficients and **the** binomial theorem to Europe. He invented many mechanical devices, including combination locks, gyroscopes with three degrees of freedom, and drive shafts (or Cardan shafts) that are still used in vehicles today. links:
- title: Imaginary Numbers
url: /world/Real_Irrational_Imaginary
cauchy:
born: 1789
died: 1857
name: Cauchy
small: true
bio: |
Augustin-Louis Cauchy (1789 – 1857) was a French mathematician and physicist. He contributed to a wide range of areas in mathematics, and
dozens of theorems and named after him.
.......
Should read as follows:
cauchy:
born: 1789
died: 1857
name: Cauchy
small: true
bio: |
Augustin-Louis Cauchy (1789 – 1857) was a French mathematician and physicist. He contributed to a wide range of areas in mathematics, and
dozens of theorems are named after him.
.....
cavalieri:
name: Cavalieri
born: 1598
died: 1647
bio: |
Bonaventura Cavalieri (1598 – 1647) was an Italian mathematician and monk. He developed a precursor to infinitesimal calculus, and is remembered
for Cavalieri's principle to find the volume of solids in geometry.
Cavalieri also worked **optics and motion, introduction logarithms to Italy,** and exchanged many letters with Galileo Galilei. links:
- title: Cavalieri's Principle
url: /course/circles/spheres-cones-cylinders#cavalieri
Should read as follows:
cavalieri:
name: Cavalieri
born: 1598
died: 1647
bio: |
Bonaventura Cavalieri (1598 – 1647) was an Italian mathematician and monk. He developed a precursor to infinitesimal calculus, and is remembered
for Cavalieri's principle to find the volume of solids in geometry.
Cavalieri also worked **in** optics and motion, **introduced** logarithms to Italy, and exchanged many letters with Galileo Galilei. links:
- title: Cavalieri's Principle
url: /course/circles/spheres-cones-cylinders#cavalieri
diophantus:
born: 200
died: 284
name: Diophantus
overflow: true
bio: |
Diophantus was a Hellenistic mathematician who lived in Alexandria.
Most of his works are about solving polynomial equations with several unknowns. These are now called Diophantine equation and remain an
an important area of research today.
It was while reading one of Diophantus' books, many centuries later, that _Pierre de Fermat_ proposed one of these equations had no solution. This became known as "Fermat's Last Theorem", and was only solved in 1994. Should read as follows:
diophantus:
born: 200
died: 284
name: Diophantus
overflow: true
bio: |
Diophantus was a Hellenistic mathematician who lived in Alexandria.
Most of his works are about solving polynomial equations with several unknowns. These are now called Diophantine equations and remain an
an important area of research today.
It was while reading one of Diophantus' books, many centuries later, that _Pierre de Fermat_ proposed one of these equations had no solution. This became known as "Fermat's Last Theorem", and was only solved in 1994. fuller:
name: Fuller
bio: Richard Buckminster "Bucky" Fuller (1895 – 1983) was an American
architect, designer and inventor. He is famous for constructing geodesic
dome – large, spherical structures. Similar looking Carbon molecules, the
fullerenes, were later named after him.
Should read as follows:
fuller:
name: Fuller
born: 1895
died: 1983
bio: Richard Buckminster "Bucky" Fuller (1895 – 1983) was an American
architect, designer and inventor. He is famous for constructing geodesic
dome – large, spherical structures. Similar looking carbon molecules, the
fullerenes, were later named after him.
galois:
**While still in his teens, Galois proved that there is no general solution for polynomial equations of degree five or higher – simultaneously with Niels Abel.** At the age of 21, Galois was shot in a duel (some say a feud over a woman),
and later died of his wounds. In the night before his death, he summarised
his mathematical discoveries in a letter to a friend. It would take other mathematicians many years to fully realise the true impact of his work.
could read:
While still in his teens, Galois, along with Niels Abel, proved that there is no general solution
for polynomial equations of degree five or higher.
At the age of 21, Galois was shot in a duel (some say a feud over a woman),
and later died of his wounds. On the night before his death, he summarised
his mathematical discoveries in a letter to a friend. It would take other mathematicians many years to fully realise the true impact of his work.
planck:
name: Plank
bio: Max Plank (1858 – 1947) was a German physicist and one of the
original developers of Quantum Mechanics – for which received the Nobel
Prize in 1918.
Should read as follows:
planck:
name: Plank
born: 1858
died: 1947
bio: Max Plank (1858 – 1947) was a German physicist and one of the
original developers of Quantum Mechanics – for which he( received the Nobel
Prize in 1918.
Interactive: Polyhedra cross-sections
A THREE.js component that visualises the cross-sections of different polyhedra, for the Polyhedra course.
Students can select from a few different pre-selected polyhedra (platonic solids, prisms and pyramids), which are arbitrarily rotatable by dragging. Students also have a slider to change the "distance" of the polyhedron from a horizontal place, which it can pass through.
If the polyhedron intersects the plane, highlight the shape of the cross-section. For example, you can make a hexagon by appropriately positioning a cube.
Essentially, a virtual version of MoMath's Wall of Fire.
hypotenuse - longest side
ENHANCEMENT
When the hypotenuse is mentioned here:
https://mathigon.org/course/triangles/pythagoras
Add the fact that it is the longest side?
Mathematics New Golden Age Pdf Github
Source: https://githubhelp.com/mathigon/textbooks
Posted by: ramirezblaideselly.blogspot.com
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