tl;dr: Want to learn maths and physics using a computer to do workings out (graphing, equation solving, problem solving) with as little use of pen and paper as possible. SMath seems like a good little program to meet at least some of my needs. SMath usage questions at the bottom of post.

I've always disliked using pen and paper. It slows me down considerably, saps a lot of my concentration energy rather quickly, and I'm hopeless at both setting my work out in a system that both I and others can understand. Going back over old working outs in high school maths with pen and paper, I would find it difficult to follow my own work, never mind my poor teachers. My learning suffered due to the inefficiencies I never overcame with using pen and paper. I did finish high school - VCE with Math Methods as a subject in which I earned a pass, and an overall tertiary entrance rank above average.

Fast forward 7 years, I've made the decision to enter university to study Medical Radiation Science. I need to have at least a basic grasp of physics and maths, and I need a method of doing workings out for exercise questions in physics and maths that is efficient. I want to do away with traditional pen and paper and go as paperless as possible, with maybe some rough workings out such as arithmetic or input from a tutor on pen and paper. Using a touch screen with a stylus on a blank document to do handwriting of everything on the computer, basically the same as pen and paper except in a digitised format, is not what I'm after, I'm looking for a solid structure provided by a computer to work within to make it much easier to set out my workings in a clear and easy to understand and follow method.

A rich environment with a pen-and-paper like interface with support for styluses on touch screens for quickly handwriting equations to convert to text and for drawing graphs, step by step guides for different areas of maths and physics (like how to figure out how much work has been done, how to solve quadratic equations) and reference sheets like one page cheat sheets we were allowed for maths exams in high school would be ideal. That's what I'd really love to see available. But this program doesn't seem to exist.

There doesn't seem to be any educational software for maths work specifically to cater to the needs of people who want to go paperless and do all their maths and physics workings on a computer. So it seems I need to develop my own method from a collection of programs and websites.


SMath seems like a good place to start to begin developing my method. It's a simple pen-and-paper like interface, it can plot graphs, and it appears to have a grid.

Here's where the usage questions start:

I want to plot a couple of simple scalar vectors. The question is like this: Sue walks 3 metres to the east, and then 5 metres to the north. What is Sue's displacement from her starting point?
How would I plot those two vectors in SMath? How would I then draw a diagonal line connecting the ends of those two vectors in order to calculate Sue's displacement from her starting point?

How do you change the scale of the 2D cartesian plot from the default 4, 8, 16 etc? I would like it to go 1, 2, 3, 4 etc.

Is there a way to draw lines within the plot free hand? This way, to answer the displacement question above, I could simply draw a line from (x,y) 0,0 to 0,3 and a line from (x,y) 0,3 to 5,3, then a diagonal line connecting the ends of these two lines which I could simply read the length of off the graph.

How do you import reference books/interactive books downloaded in .zip format into SMath? I searched the forums and Introduction to the use of SMath Studio by Gilberto E. Urroz and could not find how to do it. I ended up using the online gallery function within the Extensions Manager to redownload the Interactive SMath Handbook I want to check out.

There will be more questions to come!

What you are asking is typical of college level. My rating of college level is - 100%
wrt opening larger applied numerical stuff. For example sheets of working projects,
you are just seating on the Smath "gold mine" [you know gold mine from DownUnder].
By the time you will have exhausted Smath, your beard will be longggggg.

Any and all CAS [Computer Algebra system] have limit in the wish list.
Smath does not have a "repository", the best actual "like repository" is the forum
category [conference] "Samples".

Not long ago, I published the "Cubic Solver" in "Samples".

Cheers from "UpAbove", Jean

Wrote

What you are asking is typical of college level. My rating of college level is - 100%
wrt opening larger applied numerical stuff. For example sheets of working projects,
you are just seating on the Smath "gold mine" [you know gold mine from DownUnder].
By the time you will have exhausted Smath, your beard will be longggggg.

Any and all CAS [Computer Algebra system] have limit in the wish list.
Smath does not have a "repository", the best actual "like repository" is the forum
category [conference] "Samples".

Not long ago, I published the "Cubic Solver" in "Samples".

Cheers from "UpAbove", Jean

I get that SMath is much more powerful than the level I'm talking about, but since it's such a small program in filesize I decided to give it a try.
So do you have any suggestion of program(s) for doing the level of maths/physics I'm talking about?

Hi. Search for SMath for Physics IOP Concise Physics: A by Bernard V. Liengme.

Wrote

Hi. Search for SMath for Physics IOP Concise Physics: A by Bernard V. Liengme.

I've bought the book and have looked in it with kindle cloud reader, but I haven't yet found a solution to my usage questions.

Hello kernel

Wrote

The question is like this: Sue walks 3 metres to the east, and then 5 metres to the north. What is Sue's displacement from her starting point?

The length of a vector can be computated with the euclidean norm (wikipedia); do it for each vector you have, sum the results and you have the total displacement.

Wrote

How would I plot those two vectors in SMath? How would I then draw a diagonal line connecting the ends of those two vectors in order to calculate Sue's displacement from her starting point?

In a standard plot (type @ on the canvas) you can draw segments using matrices (x coordinates on the 1st column, y coordinates on the 2nd column); a path can be drawn with a single matrix or grouping single vectors with the sys() function (last element in the "Functions" panel on the right of your screen)

Wrote

How do you change the scale of the 2D cartesian plot from the default 4, 8, 16 etc? I would like it to go 1, 2, 3, 4 etc.

In the built-in plot is not possible. There are alternatives such as the X-Y plot available on the Extensions Manger (Tools > Plugins > Online Gallery).

Wrote

Is there a way to draw lines within the plot free hand? This way, to answer the displacement question above, I could simply draw a line from (x,y) 0,0 to 0,3 and a line from (x,y) 0,3 to 5,3, then a diagonal line connecting the ends of these two lines which I could simply read the length of off the graph.

Not available, sorry

Wrote

How do you import reference books/interactive books downloaded in .zip format into SMath?

Downloaded from the wiki? You have to go to the "%APPDATA%\SMath\extensions\" path and do the job manually, you can use a regular download as reference to build new folders of the same type. The strange names of folders are unique IDs of each extension (you have to generate your own for things not available in the gallery

Did Sue walked 3+5 = 8 meters ?
What is "displacement" in math/physics terms ?



Jean

Wrote

Hello kernel

Wrote

The question is like this: Sue walks 3 metres to the east, and then 5 metres to the north. What is Sue's displacement from her starting point?

The length of a vector can be computated with the euclidean norm (wikipedia); do it for each vector you have, sum the results and you have the total displacement.

Wrote

How would I plot those two vectors in SMath? How would I then draw a diagonal line connecting the ends of those two vectors in order to calculate Sue's displacement from her starting point?

In a standard plot (type @ on the canvas) you can draw segments using matrices (x coordinates on the 1st column, y coordinates on the 2nd column); a path can be drawn with a single matrix or grouping single vectors with the sys() function (last element in the "Functions" panel on the right of your screen)

Wrote

How do you change the scale of the 2D cartesian plot from the default 4, 8, 16 etc? I would like it to go 1, 2, 3, 4 etc.

In the built-in plot is not possible. There are alternatives such as the X-Y plot available on the Extensions Manger (Tools > Plugins > Online Gallery).

Wrote

Is there a way to draw lines within the plot free hand? This way, to answer the displacement question above, I could simply draw a line from (x,y) 0,0 to 0,3 and a line from (x,y) 0,3 to 5,3, then a diagonal line connecting the ends of these two lines which I could simply read the length of off the graph.

Not available, sorry

Wrote

How do you import reference books/interactive books downloaded in .zip format into SMath?

Downloaded from the wiki? You have to go to the "%APPDATA%\SMath\extensions\" path and do the job manually, you can use a regular download as reference to build new folders of the same type. The strange names of folders are unique IDs of each extension (you have to generate your own for things not available in the gallery

Brilliant, thanks very much.

Wrote

Did Sue walked 3+5 = 8 meters ?
What is "displacement" in math/physics terms ?



Jean

Sue walked 3 metres + 5 metres for a total distance traveled of 8 metres.
"Displacement" in maths/physics terms is the distance from the point of origin. If you are in place x and you walk 3 metres to the east and then 5 metres in the north and you are now in place y, as per your attached graphic, you are at a displacement from place x of about 6.56 metres as that is the distance as the bird flies from place x to place y. Thanks for that graphic, it will help me learn how to do this in SMath.

Nicholas

Wrote

Smath does not have a "repository", the best actual "like repository" is the forum
category [conference] "Samples".

The extension manager provides a way to distribute examples and code snippets. You just upload your sm-sheet with having some conventions about how to supply metadata in mind. Then all other users can access this example either in the online gallery of the extension manager from within SMath or they can access it from the smath home page (http://en.smath.info/ or button "Apps" in the forum header).

Examples are smath sheets which can be opened as separate documents, whereas snippets are meant to be pasted as a collapsed area region into the current document.

For examples which have been tested and discussed in the community, the extension manager is a far better way for sharing than the forum itself. By far not all smath users also follow the forum.

As you have quite a lot of examples from different areas of science, you might consider making an interactive book. This can be distributed via extension manager and consists of a set of interlinked smath sheets. It is a bit handwork to create the links but Davide has made a great job in supporting this work with the text region utilities.

My interactive book already contains some examples and if you want you can contribute via svn. We can discuss the details if you are interested.

Martin Kraska

Wrote

Wrote

Smath does not have a "repository", the best actual "like repository" is the forum
category [conference] "Samples".

The extension manager provides a way to distribute examples and code snippets. You just upload your sm-sheet with having some conventions about how to supply metadata in mind. Then all other users can access this example either in the online gallery of the extension manager from within SMath or they can access it from the smath home page (http://en.smath.info/ or button "Apps" in the forum header).

Examples are smath sheets which can be opened as separate documents, whereas snippets are meant to be pasted as a collapsed area region into the current document.

For examples which have been tested and discussed in the community, the extension manager is a far better way for sharing than the forum itself. By far not all smath users also follow the forum.

As you have quite a lot of examples from different areas of science, you might consider making an interactive book. This can be distributed via extension manager and consists of a set of interlinked smath sheets. It is a bit handwork to create the links but Davide has made a great job in supporting this work with the text region utilities.

My interactive book already contains some examples and if you want you can contribute via svn. We can discuss the details if you are interested.

Martin Kraska

This is off topic, could you please take it to pm?

Hello, kernel.

So, I understand that you will kiss your girl friend if
you walk the right East/North distance while she walks a
lesser diagonal distance. What happens if both of you
end in the Pacific Ocean ?

More interesting: for spot testing of the camara objective
you will have to check the symmetry of the spot...
There is more about applying a correction matrix wrt the
mapping of the sensors.... Maybe a RemToDo in Smath.

More stuff in the attached.

jean

Utilities Matrix [Times, Dia, Mirror,Euclid].sm (30 KiB) downloaded 61 time(s).

Well, that's a good point. Hopefully I won't have to take the curvature of the earth into account as it's Medical Radiation Physics I'll be studying only in the first year of the radiography degree. I think the curvature of the earth only makes a difference for long distances and when you need to make very precise measurements.

I think in this case, rather than kissing Sue she would bump into me and I would be pushed out of the way.
But I forgot to mention in the original post that this is just one object in a 2D world. Such a world is completely flat with no curvature at all, and there are no other objects to collide with.