Mathigon
@MathigonOrg
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The Mathematical Playground – making learning more interactive and engaging than ever before, and FREE for everyone. Part of @amplify
London, UK
Joined April 2012
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Archimedes discovered that if you add the volume of a cone and a sphere, you get the volume of their bounding cylinder. It’s one of the most beautiful results in 3D geometry! Learn more at
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Cartographers always have to distort the surface of Earth in order to create a flat map. Notice how the same square on a map can have many different shapes and sizes in reality:
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Isaac Newton was born 380 years ago. He in one of the greatest scientists in history: he discovered the laws of gravity and motion, invented calculus, built the first reflecting telescope, split white light into the visible spectrum, and so much more.
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Cartographers always have to distort the surface of Earth in order to create a flat map. Notice how the same square on a map can have many different shapes and sizes in reality. Explore for yourself at
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Different map projections distort the surface of Earth in different ways – which means that a square on a map is not always a square in real life!
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BREAKING: Mathematicians have found an exact fraction that equals π, thereby disproving the long-standing conjecture that π is irrational. We now know that π = 1783366216531/567663097408. Learn more at
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Emmy Noether was born 141 years ago
#onthisday
! She discovered how the symmetries of our universe correspond to conserved quantities in physics and thus can explain the most fundamental laws of nature. Learn more at
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Archimedes discovered that if you add the volume of a cone and a sphere, you get the volume of their bounding cylinder. It’s one of the most beautiful results in 3D geometry! Learn more at
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Big news: Polypad now supports 3D geometry! 🎉⚽️🎁 Use one of our built-in solids, or create your own net using polygon tiles. Then click “fold” and watch the magic happen…
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Archimedes discovered that if you add the volume of a cone and a sphere, you get the volume of their bounding cylinder. It’s one of the most beautiful results in 3D geometry!
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Today is a big day for mathematics: Pi Day, the first ever International Day of Mathematics, as well as Albert Einstein’s 141st birthday.
#PiDay
#IDM314
#MathematicsDay
#math
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Évariste Galois died at the age of 20, after being shot in a duel. In his short life, he laid the foundation for two entirely new areas of mathematics: group theory and Galois theory. He was born 211 years ago
#onthisday
. Learn more at
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BREAKING: Mathematicians have found an exact fraction that equals Pi, thereby disproving the long-standing conjecture that Pi is irrational. We now know that π = 1783366216531/567663097408. Learn more at
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Carl Friedrich Gauss, born 245 years ago
#onthisday
, was one of the greatest mathematicians in history. He made groundbreaking discoveries in every area of maths, physics, and astronomy, and mentored many other important mathematicians. Learn more at
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Polypad is the ultimate collection of virtual manipulatives: polygons, number and algebra tiles, fraction bars, tangram, and much more. It works on all devices, has been translated into 16 languages, and is completely free to use.
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We'll close 2021 with our most popular post of the year. We look forward to continuing to explore mathematics with you in 2022!
#math
#mtbos
#mathchat
#edchat
Cartographers always have to distort the surface of Earth in order to create a flat map. Notice how the same square on a map can have many different shapes and sizes in reality:
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Blaise Pascal was a mathematician, physicist, and philosopher and was born 400 years ago today. He invented one of the first mechanical calculators, worked on geometry, probability, physics, and theology. Learn more at
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Tiny differences in the initial conditions of a double pendulum quickly get amplified and lead to a completely different motion. Learn more about chaos theory and its applications at
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Évariste Galois died at the age of 20, after being shot in a duel. In his short life, he laid the foundation for two entirely new areas of mathematics: Group theory and Galois theory. He was born 209 years ago
#onthisday
.
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Julia Sets are special fractals generated by checking if a recursive sequence diverges at different starting points on the complex plane. You can create them yourself at
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Archimedes discovered that if you add the volume of a cone and a sphere, you get the volume of their bounding cylinder. It’s one of the most beautiful results in 3D geometry! Learn more at .
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All flat maps have to distort the surface of Earth in some way. Notice how the same square on a map can have many different shapes and sizes in reality! 🌍 🗺️
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The Mandelbrot set can be created using the simple recursive equation x(n) = x(n–1)² + c, but it is infinitely complex and contains new patterns at every zoom level. Learn more about this famous fractal at
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Splitting up a circle into rings and then rearranging those rings to attempt to make a triangle is one way to investigate the formula for the area of a circle. Explore this idea further at
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Cartographers always have to distort the surface of Earth in order to create a flat map. Notice how the same square on a map can have many different shapes and sizes in reality. Explore for yourself at
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Archimedes discovered that if you add the volume of a cone and a sphere, you get the volume of their bounding cylinder. It’s one of the most beautiful results in 3D geometry!
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Leonard Euler was born 314 (π-hundred!) years ago
#onthisday
. He invented graph theory, pioneered calculus, developed our modern mathematical notation, and also worked on fluid dynamics, optics, music theory and astronomy. His combined works fill 80 books!
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Next week is International Women’s Day. We’ve created an all-female version of our timeline of mathematics – from Hypatia to Mirzakhani. Download a high-res version at
#ChooseToChallenge
#IWD2021
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A brand new trailer for Mathigon – see all our favourite games and activities in action!
#mathclass
#mtbos
#edchat
Full-length version at
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Practice your problem-solving skills with our huge library of challenging mathematical puzzles – from geometry to algebra, number theory, logic and probability:
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Next week, we are starting our annual puzzle calendar, with 24 challenging problems. Get ready by trying some of the puzzles from previous years:
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Carl Friedrich Gauss, born 246 years ago
#onthisday
, was one of the greatest mathematicians in history. He made groundbreaking discoveries in every area of maths, physics, and astronomy and mentored many other important mathematicians. Learn more at
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Joseph Fourier was born 254 years ago
#onthisday
. The French mathematician and physicist invented Fourier series to explain vibrations and heat transfer. He also discovered the Greenhouse effect! Learn more at
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Are you looking for something to keep you busy this summer vacation? Why not explore our puzzle calendars with 96 challenging questions!
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Cartographers have to cheat when creating maps, because the surface of Earth is curved. There are many different projections, all of which distort the surface in different ways:
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Start with 100 dice, roll all of them, delete all sixes, and repeat. How long until there are no more dice left? How is this related to exponential functions, radioactive decay, and carbon dating?
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Our Polypad task library now contains more than 80 lesson plans, tutorials, puzzles, games and teaching ideas – covering the entire K-12 curriculum. They are completely free, and we’re always adding more:
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Polypad: Discover the ultimate mathematical playground!
🧮 30+ Virtual manipulatives
🖋️ Powerful digital whiteboard
📏 Dynamic geometry tools
📤 Effortless sharing + assigning
📱 Mobile, touch and offline support
🗺️ 19 Languages, WCAG accessible
🎉 COMPLETELY FREE
(Sound on 🔊)
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📣 We’re super excited to reveal a brand new library of lesson plans, tasks, tutorials, puzzles and activities for Polypad! Explore more than 50 free resources, with many more coming soon, at
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These interactive animations show how you can find the surface area of cylinders and cones, by “unrolling” their net:
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Where do circles, ellipses, hyperbolas, and parabolas like to hang out in the summer? Coney Island!
You can make many different shapes by pointing a light cone onto a flat surface. They might look different but have many common properties. Learn more at
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69 years ago today, Edmund Hillary and Tenzing Norgay reached the top of Mount Everest. More than a century earlier, mathematicians used trigonometry to calculate its precise height. Learn more at
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Leonardo Fibonacci’s “Liber Abaci” is one of the most influential books in history: it first introduced Arabic numerals to Europe, explains how merchants can use algebra to calculate profits and interest, and investigates the famous Fibonacci numbers.
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Prime factor diagrams in Polypad! Simply drag to separate numbers into their factors, or recombine them into larger numbers. 🤯
@MathforLove
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Leonard Euler was born 315 years ago
#onthisday
! He invented graph theory, pioneered calculus, developed our modern mathematical notation, and worked on fluid dynamics, optics, music theory, and astronomy. His combined works fill 80 books! Learn more at
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"Pascal's" triangle has been studied by people around the world, including some that came long before Pascal. In India, it was known as the “Staircase of Mount Meru”. In Persia, the “Khayyam triangle”, and in China, “Yang Hui’s triangle”. Learn more at
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Today is a huge day for mathematics!
(1) Pi Day 🥧
#PiDay
(2) International Day of Mathematics 🎉
#idm314
(3) Albert Einstein’s 142nd birthday 👨🔬
#onthisday
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Whether remotely or in classrooms, don’t go
#BackToSchool
without the Textbook of the Future! Mathematics has never been so interactive and engaging.
🧮 Virtual manipulatives
📚 Interactive courses + games
📱 All devices + works offline
🗺️ 18 languages
🎉 FREE for everyone!
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The Greek philosopher Plato believed that all matter in the universe consisted of “Platonic solids,” a set of regular polyhedra. It turns out there are just five of them – but why? Learn more at
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Five tetrahedra, each in a different color and each made with 30 sheets of paper with no scissors or glue, intersect to form this Origami creation. Find the instructions for this and many more Origami models at .
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We hope you enjoyed our puzzle calendar! All 24 problems and solutions can now be found at
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Regular pentagons don't tessellate – but there are 15 other types of pentagons that do. We’ve collected all of them at . Can you fit them together?
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Many of you have asked for this feature: Polypad now contains polyhedral dice! 🎲
(And we'll more 3D tools over the summer…)
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The hundreds of tools, features and manipulatives available at make online learning more interactive than ever before – and they are completely free. What can you create?
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Simply by moving two points, we can create self-similar fractals that looks like ferns, trees, nested pentagons, and many other shapes. What else can you discover?
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In honour of International Women’s Day, here are twelve of the most important female mathematicians:
#EachforEqual
#IWD2020
#WomenInStem
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Leonardo Fibonacci’s “Liber Abaci” is one of the most influential books in history: it first introduced Arabic numerals to Europe, explains how merchants can use algebra to calculate profits and interest, and investigates the famous Fibonacci numbers.
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The Sieve of Eratosthenes is a simple method for finding prime numbers: you highlight the next available number and then cross out all of its multiples. How many primes are there less than 100? Try for yourself at
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Go
#BackToSchool
with the ultimate mathematical playground!
🧮 Best-in-class virtual manipulatives
📐 Graphing, geometry and data science
🎓 Sharing, assigning and collaboration
🎬 100+ lesson plans and videos for K12
🗺️ Supports all devices + 23 languages
🎉 Completely FREE
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David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss recently discovered an aperiodic monotile! Try tiling the plane with this tile at .
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Have you seen the new Function Machines on Polypad? Try them for yourself at and learn more about them in this Polypad Pointer video:
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For our friends in Canada, we now have Canadian coins on Polypad!
🇨🇦🇨🇦🇨🇦 $ $ $ 🇨🇦🇨🇦🇨🇦
Explore all the coin options on Polypad at
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Regular polyhedra that consist of multiple different types of polygons are called Archimedean solids – and there are just 13 of them. Can you see which one consists of pentagons and hexagons, just like a football?
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This tennis ball loses a fixed proportion of its height with every bounce. Do you know what type of sequence is formed by listing the resulting maximum heights from each bounce? Learn more at
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The Balance Scale is one of the most versatile tools on Polypad. Watch our latest Polypad Pointer video to learn how to use the scale with algebra tiles, polygons, dice and even imported images!
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All repeated, 2-dimensional patterns have one of 17 different symmetries. These are called the “Wallpaper Groups”, and you can explore all of them at
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Big news! Mathematicians have finally found a counterexample to disprove Fermat's Last Theorem: 3987^12 + 4364^12 = 4472^12!
Watch
@SLSingh
explain the details in this video:
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We just released some new
#datascience
tools for Polypad! Create row, column, line, area, pie and donut charts, as well as box plots, by linking a table with your data. 📊📈 Histograms, scatter plots, and probability distributions will be next!
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Our interactive, 3D diagrams allow students to derive equations for the surface area of cylinders, cones and other solids:
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The French mathematician and philosopher René Descartes was born 427 years ago. He developed the “cartesian” coordinate system, which is named after him. His work also provided the foundations for discovering calculus a few decades later. Learn more at
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If you highlight all multiples of a number in Pascal’s triangle, beautiful patterns emerge. What do you notice or wonder? Try our interactive version at
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Visual patterns are a fantastic way to introduce algebra. We’ve used Polypad to create interactive version of 20+ different patterns designed by
@fawnpnguyen
:
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We hope you enjoyed our puzzle calendar! All 24 problems and solutions can now be found at
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Today is the birthday of two great mathematicians. Maryam Mirzakhani studied objects like hyperbolic surfaces and complex manifolds. She was particularly fascinated by the beauty of mathematics, and received the Fields Medal in 2014. Learn more here:
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On Polypad, we've just added the ability to cut polygons into multiple parts! ✂️✂️✂️
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Tessellations appear everywhere in nature, art and architecture. Discover why some shape tessellate while others don’t, and create your own patterns, at
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We've just published a big update to our timeline of mathematics, including
• 19,000 more years of history before ancient Greece
• Historical artefacts from different civilisations
• Many more female mathematicians
What/who else do you want to see?
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Évariste Galois died at the age of 20, after being shot in a duel. In his short life, he laid the foundation for two entirely new areas of mathematics: group theory and Galois theory. He was born 211 years ago
#onthisday
. Learn more at
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DAY 21: How many triangles are in this diagram?
All puzzles and solutions at
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Just like there are 5 axioms of Euclidean geometry, there are 7 “Origami axioms” which describe everything that’s possible when folding paper:
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Bernhard Riemann was born 197 years ago today. Amongst many other achievements, he made groundbreaking discoveries about the distribution of prime numbers. The “Riemann hypothesis” is still one of the most important unsolved problems in math. Learn more at
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Pascal’s triangle has been studied for thousands of years, by mathematicians all around the world. In India, it was known as the “Staircase of Mount Meru”. In Persia it was called the “Khayyam triangle”, and in China it was “Yang Hui’s triangle”. More at
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Can you draw a path that crosses every bridge once, but not more than once? Leonard Euler solved this puzzle more than 200 years ago by inventing graph theory. Today, this subject has applications in science, technology and engineering. Try it out at
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The Dutch artist M. C. Escher was born 124 years ago
#onthisday
. He was constantly inspired by mathematical ideas, like tessellations, polyhedra, hyperbolic geometry, or impossible shapes. Learn more at
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As we write new courses for Mathigon, we have collected a set of nine principles for creating great mathematics content: from storytelling to visualisations. You can read more at
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Start with 100 dice. Roll them and remove all the sixes. Repeat until there are 25 or less dice left. How many rounds will this take? Learn more about exploring this idea with students in this Polypad Pointer video:
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One way to find the formula for the volume of a sphere is to compare its cross section to that of a cylinder with a cut-out cone in its center. Learn more at .
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Our annual puzzle calendar begins tomorrow! We'll post a puzzle here each day as well as at . Solutions will be posted on our site 24 hours later. We hope you enjoy the collection the year!
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Georg Cantor was born 179 years ago
#onthisday
. One of the greatest mathematicians in history, he invented set theory and discovered that there are “different sizes” of infinity. Learn more at
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The 3D diagrams in our interactive courses allow students to derive equations for the surface area of cylinders, cones and other solids. Explore all the interactives at
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Have you played Factris yet? This fun game incorporates ideas of simple arithmetic, divisibility, factors and prime numbers. For maximum points, clear as many rows as possible at once. Share a screenshot of your score! Can you reach the high score? Play at
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