I used Desmos quite a bit as an instructional tool for high school math. They are funded through relationships with several companies, but most notably the standardized testing industry, which uses it with their online tests.
Over ten years before Desmos launched, there began an open source project called Geogebra (https://www.geogebra.org/). Geogebra remains open source to this day and offers a similar suite of applications and calculators, both online and in app form.
Over the years I have also used Geogebra as an instructional tool in both my math and physics classrooms, producing dozens of apps, simulators, and gizmos: https://www.geogebra.org/u/mrdathhs
Geogebra excels at creating mathematical simulations. One of my favorites was this real-time satellite orbit calculator: https://www.geogebra.org/m/UEynuRnG
I, too, use both Desmos and Geogebra in my classroom. One of my favourite things about Geogebra is the ability to export to tikz. It can save a lot of time when making complex geometry problems while keeping things nice and neat in your latex file. I also like using the Geogebra 3D AR app to get kids to see the different ways planes intersect, and what a parameterized solution “looks like” in a 3x3 system. It makes for a lot of “aha” moments.
On the other hand Desmos is quick, easy to use, and looks nice. The test-mode app works well on phones and the College Board will be using it for their AP exams this year, so they must be doing something right. Their new 3D apps look promising but I haven’t played with them much, yet.
Both tools have their place, but my heart is 100% with Geogebra.
> Please note that GeoGebra as a complete software program would probably not be considered "free" software according to the definition of that term which is used by the Free Software Foundation. This is because the restrictions on commercial use that apply to the GeoGebra installers, web services and language files add-ons might be seen to be a restriction on the software as a whole (thus making it "non-free"), even though the GeoGebra source code is made available under the GNU General Public License without restriction. You can rest assured that our license terms fully respect all existing licenses from third parties (including the GNU General Public License and all Creative Commons variants) and have been checked by an experienced law firm.
Note that "the GeoGebra source code is made available under the GNU General Public License without restriction"
I don't see how this is a contradiction in itself. It is very similar to dual-licensing for commercial use.
I really wish I could get a dedicated handheld graphing calculator that hasn't had most of the functionality removed due to standardized testing. We live in an age of miracles but having a decent solver on a dedicated device is apparently commercially impossible because it couldn't be sold to students.
I'm just a dude in my shop that occasionally would like to integrate a thing or two without getting coolant on my phone.
There is DM42 hardware[1] and the DB48X/C47 firmwares for it. I feel that they are very much pushing the boundary on what makes sense on a formfactor like that.
For something more powerful, you'd probably want something more in the "cyberdeck" direction, with some 3d printing and cheap ARM linux boards it's relatively easy to build portable distraction-free compute device.
I adore this Micro Journal device[2]. Although it's intended for writing, it's not too difficult to imagine it running some suitable calculator software. The keyboard could be easily adapted to HP Voyager (15c etc) style layout.
HP Prime G2 can certainly graph things, evaluate integrals, solve systems of equations etc not sure how hard you’re looking because all the manufacturers have models like that. They have an exam mode which nerfs the calculator for tests.
If you'd rather get coolant on a dedicated device, there are some insanely good mobile calculator apps—and desmos' site or mobile app. You can install them on a virtually limitless range of devices.
The TI-Nspire CX CAS II, Casio ClassPad fx-CP400, and HP Prime G2 are the main CAS-enabled calculators available these days. The TI-89 Titanium and HP-50G are also options, albeit older models (with the HP-50G being discontinued).
I posted on Mastodon today about how helpful tools like this are for building mathematical intuition. Animations are no substitute, but they can also do what lecture never could.
Since my current project has pretty much devolved to putting a UI on various trigonometric functions and allowing the user to program them, I'd be very glad of other resources in this space (currently working through Hilbert's _Geometry and the Imagination_ and the book which matches https://projectivegeometricalgebra.org/ and just finished the _Make:Geometry/Trigonometry/Calculus_ series, and have had recommended Curves and Surfaces for CAGD: A Practical Guide by Gerald Farin)
Desmos also produces curriculum for K-12 (Desmos Classroom) that takes advantage of the computer’s ability to give real-time feedback for student answers beyond just giving them a binary correct/incorrect. It shows them what their wrong answers really would mean in the little animated scenario. Good stuff!
High school students taking the digital SAT get near-full access to Desmos throughout the math portion of the test (it’s a modified version, but you get access to practically everything). It’s very powerful, and if you can use it effectively, you can brute force hard questions in seconds. Graphing calculators have been available during the SAT in the past, but Desmos is something else… I wonder how it effects score distributions/question difficulty.
and on the topic of calculators in high school maths, the NumWorks calculator is so far ahead of the TI-84 despite being allowed on the same tests. It honestly feels like an advantage over my peers… it can literally do more, and faster. It was a big shock when I realized handheld calculators don’t have to suck. Highly recommend.
On the TI-84, there was a lot of great third-party software you could load onto the calculator. When I was in school, I had a fair few useful and not-so-useful things loaded onto my TI-84, including a copy of Symbolic, which gave the TI-84 some limited symbolic calculus functionality. I don't remember much else of what I had. Rather than use the calculator to help with repetitive math, though, what I really wound up doing most of the time is messing around in TI Basic instead of doing my work.
I spent a long time trying to figure out how to make TI Basic programs fast enough to do games. Graph drawing commands were too slow!
I realized that for most things text was the right way to go, but eventually I did manage to make a facsimile of Pong that was decently fast in graph mode by simply drawing each frame incrementally rather than clearing and redrawing it each time. Pretty obvious in retrospect, but I was still relatively new to programming when I first started messing with TI Basic.
I also struggled to write shared routines with only goto, so my code was a catastrophic mess. I assume most TI Basic code was, though.
Ooh, that’s pretty neat! When I took the SAT (not all that long ago) they wouldn’t even let me bring in my TI-89 :( Out of spite I used my fx-115 ES-PLUS through it instead (which is honestly better in most ways, despite being a scientific calculator).
Awesome. I love desmos. I just used it yesterday for a Wave mathematics class I taught for a homeschool group. I also wrote a math graphing program that helps make math beautiful called [Truthy Graph](https://truthygraph.github.io/). It came from a thought: most graphing programs only graph were both sides of the equation are exactly equal, but what would it look like to see also where they are nearly equal (in other words, the error gradient)?
For a similar project in a similar space (but with both a free android emulator, and the option for a dedicated hardware device), see [0]. I actually use it as my preferred calculator on my phone.
We are in kind of similar category but broader data literacy space and making data analysis more accessible and interactive. give it a try at https://tuvalabs.com
you can plot functions on top of your visualizations, or take samples etc.
I used Desmos quite a bit as an instructional tool for high school math. They are funded through relationships with several companies, but most notably the standardized testing industry, which uses it with their online tests.
Over ten years before Desmos launched, there began an open source project called Geogebra (https://www.geogebra.org/). Geogebra remains open source to this day and offers a similar suite of applications and calculators, both online and in app form.
Over the years I have also used Geogebra as an instructional tool in both my math and physics classrooms, producing dozens of apps, simulators, and gizmos: https://www.geogebra.org/u/mrdathhs
Geogebra excels at creating mathematical simulations. One of my favorites was this real-time satellite orbit calculator: https://www.geogebra.org/m/UEynuRnG
I, too, use both Desmos and Geogebra in my classroom. One of my favourite things about Geogebra is the ability to export to tikz. It can save a lot of time when making complex geometry problems while keeping things nice and neat in your latex file. I also like using the Geogebra 3D AR app to get kids to see the different ways planes intersect, and what a parameterized solution “looks like” in a 3x3 system. It makes for a lot of “aha” moments.
On the other hand Desmos is quick, easy to use, and looks nice. The test-mode app works well on phones and the College Board will be using it for their AP exams this year, so they must be doing something right. Their new 3D apps look promising but I haven’t played with them much, yet.
Both tools have their place, but my heart is 100% with Geogebra.
Sadly this isn't really Free Software: https://www.geogebra.org/license
Open Source only for non-commercial use is a contradiction in itself.
They call this out in their license explicitly
> Please note that GeoGebra as a complete software program would probably not be considered "free" software according to the definition of that term which is used by the Free Software Foundation. This is because the restrictions on commercial use that apply to the GeoGebra installers, web services and language files add-ons might be seen to be a restriction on the software as a whole (thus making it "non-free"), even though the GeoGebra source code is made available under the GNU General Public License without restriction. You can rest assured that our license terms fully respect all existing licenses from third parties (including the GNU General Public License and all Creative Commons variants) and have been checked by an experienced law firm.
Note that "the GeoGebra source code is made available under the GNU General Public License without restriction"
I don't see how this is a contradiction in itself. It is very similar to dual-licensing for commercial use.
I really wish I could get a dedicated handheld graphing calculator that hasn't had most of the functionality removed due to standardized testing. We live in an age of miracles but having a decent solver on a dedicated device is apparently commercially impossible because it couldn't be sold to students.
I'm just a dude in my shop that occasionally would like to integrate a thing or two without getting coolant on my phone.
There is DM42 hardware[1] and the DB48X/C47 firmwares for it. I feel that they are very much pushing the boundary on what makes sense on a formfactor like that.
For something more powerful, you'd probably want something more in the "cyberdeck" direction, with some 3d printing and cheap ARM linux boards it's relatively easy to build portable distraction-free compute device.
I adore this Micro Journal device[2]. Although it's intended for writing, it's not too difficult to imagine it running some suitable calculator software. The keyboard could be easily adapted to HP Voyager (15c etc) style layout.
[1] https://www.swissmicros.com/product/model-dm42n
[2] https://liliputing.com/micro-journal-rev-2-revamp-is-a-compa...
HP Prime G2 can certainly graph things, evaluate integrals, solve systems of equations etc not sure how hard you’re looking because all the manufacturers have models like that. They have an exam mode which nerfs the calculator for tests.
If you'd rather get coolant on a dedicated device, there are some insanely good mobile calculator apps—and desmos' site or mobile app. You can install them on a virtually limitless range of devices.
TI has CAS enabled variants of their calculators.
The TI-Nspire CX CAS II, Casio ClassPad fx-CP400, and HP Prime G2 are the main CAS-enabled calculators available these days. The TI-89 Titanium and HP-50G are also options, albeit older models (with the HP-50G being discontinued).
Have you looked at some of the alternative firmwares for older Numworks models?
I posted on Mastodon today about how helpful tools like this are for building mathematical intuition. Animations are no substitute, but they can also do what lecture never could.
Mastodon post: https://mastodon.social/@sonicrocketman/113884920858897541
A wonderful example of this is:
The Continuity of Splines https://www.youtube.com/watch?v=jvPPXbo87ds
and
The Beauty of Bézier Curves https://www.youtube.com/watch?v=aVwxzDHniEw
by Freya Holmér https://www.youtube.com/@acegikmo
While not animated, I find:
_Euclid's Elements_ (Joyce's Java Version) very helpful https://mathcs.clarku.edu/~djoyce/java/elements/elements.htm...
Since my current project has pretty much devolved to putting a UI on various trigonometric functions and allowing the user to program them, I'd be very glad of other resources in this space (currently working through Hilbert's _Geometry and the Imagination_ and the book which matches https://projectivegeometricalgebra.org/ and just finished the _Make:Geometry/Trigonometry/Calculus_ series, and have had recommended Curves and Surfaces for CAGD: A Practical Guide by Gerald Farin)
Freya Holmér is great.
To add on: Grant Sanderson's 3Blue1Brown youtube channel might be the best conceptual math presentation in history, the animations are incredible.
Desmos also produces curriculum for K-12 (Desmos Classroom) that takes advantage of the computer’s ability to give real-time feedback for student answers beyond just giving them a binary correct/incorrect. It shows them what their wrong answers really would mean in the little animated scenario. Good stuff!
https://danmeyer.substack.com/p/the-only-question-you-need-t...
How can we animate in Desmos?
I'm trying to animate t in a parametric curve (Lissajous) (sin(2*t*PI), sin(t*PI))
Example Lissajous animation https://ericfortis.github.io/lissajous/
High school students taking the digital SAT get near-full access to Desmos throughout the math portion of the test (it’s a modified version, but you get access to practically everything). It’s very powerful, and if you can use it effectively, you can brute force hard questions in seconds. Graphing calculators have been available during the SAT in the past, but Desmos is something else… I wonder how it effects score distributions/question difficulty.
and on the topic of calculators in high school maths, the NumWorks calculator is so far ahead of the TI-84 despite being allowed on the same tests. It honestly feels like an advantage over my peers… it can literally do more, and faster. It was a big shock when I realized handheld calculators don’t have to suck. Highly recommend.
On the TI-84, there was a lot of great third-party software you could load onto the calculator. When I was in school, I had a fair few useful and not-so-useful things loaded onto my TI-84, including a copy of Symbolic, which gave the TI-84 some limited symbolic calculus functionality. I don't remember much else of what I had. Rather than use the calculator to help with repetitive math, though, what I really wound up doing most of the time is messing around in TI Basic instead of doing my work.
I got in trouble for programming on my calculator in my high school computer class, lol
I spent a long time trying to figure out how to make TI Basic programs fast enough to do games. Graph drawing commands were too slow!
I realized that for most things text was the right way to go, but eventually I did manage to make a facsimile of Pong that was decently fast in graph mode by simply drawing each frame incrementally rather than clearing and redrawing it each time. Pretty obvious in retrospect, but I was still relatively new to programming when I first started messing with TI Basic.
I also struggled to write shared routines with only goto, so my code was a catastrophic mess. I assume most TI Basic code was, though.
Ooh, that’s pretty neat! When I took the SAT (not all that long ago) they wouldn’t even let me bring in my TI-89 :( Out of spite I used my fx-115 ES-PLUS through it instead (which is honestly better in most ways, despite being a scientific calculator).
Awesome. I love desmos. I just used it yesterday for a Wave mathematics class I taught for a homeschool group. I also wrote a math graphing program that helps make math beautiful called [Truthy Graph](https://truthygraph.github.io/). It came from a thought: most graphing programs only graph were both sides of the equation are exactly equal, but what would it look like to see also where they are nearly equal (in other words, the error gradient)?
For a similar project in a similar space (but with both a free android emulator, and the option for a dedicated hardware device), see [0]. I actually use it as my preferred calculator on my phone.
All the best,
[0] https://www.numworks.com/
They or someone should build one using Desmos.
If you're interested in conlangs, someone made a language, Grapherit [0], that is "spoken" via the Desmos graphing calculator.
[0]: https://m.youtube.com/watch?v=HP3nIDAhwYo
Some past comments, https://news.ycombinator.com/item?id=37859085
Thanks! Macroexpanded:
Desmos 3D graphing calculator - https://news.ycombinator.com/item?id=37859085 - Oct 2023 (83 comments)
How Desmos uses Pratt Parsers (2018) - https://news.ycombinator.com/item?id=36245786 - June 2023 (19 comments)
More Intuitive Calculator Arithmetic (2018) - https://news.ycombinator.com/item?id=21330341 - Oct 2019 (21 comments)
Visual Demonstration of Approximating Arbitrary Functions with Sigmoids - https://news.ycombinator.com/item?id=19711416 - April 2019 (1 comment)
How Desmos uses Pratt Parsers - https://news.ycombinator.com/item?id=18903550 - Jan 2019 (6 comments)
Reign of the $100 graphing calculator is ending - https://news.ycombinator.com/item?id=14298375 - May 2017 (72 comments)
Desmos Graphing Calculator – HTML5 with LaTeX editor - https://news.ycombinator.com/item?id=11369540 - March 2016 (29 comments)
Not Desmos but related https://graphtoy.com/
Made by Inigo Quilez
Desmos is a great tool a nice trick I learned late during my undergrad is that desmos copy/paste gives Latex
So a pretty well featured latex equation builder is always a click away if you’ve got a graphing calculator bookmarked in your browser
Same thing with symbolab if I recall and a handful of other web based math tools
Some crazy hacker has even used the calculator UI to implement a Sudoku game: https://www.desmos.com/calculator/vg3vye1rvm
I'm learning about digital signal processing and I use Desmos all the time as a scratchpad to plot the response of functions.
Desmos completely founded my understanding of how many things in digital signal processing work. For example convolution or time delays
We are in kind of similar category but broader data literacy space and making data analysis more accessible and interactive. give it a try at https://tuvalabs.com
you can plot functions on top of your visualizations, or take samples etc.
https://www.desmos.com/art
https://www.desmos.com/geometry/5shw8dydms
I'm not much of a math aficionado, but I tip my hat to the creator of Desmos. Has been around and free for quite awhile now.
I love Desmos. It's been a valuable tool over the years for all sorts of things, many of which were game design related.
Does it do 3d?