Function app — Signed Area

[cdmackay]

Helping my daughter with her homework gave me the chance to play with some of the Function app's Plot functions, which I'd not used before.

The Signed Area function is great, which gives the area under one function and above another (or the X-axis) between two points.

However, one thing I thought could be easier, would be a quicker way to select the two end-points as intersection points of the functions. That's because the Function app's Results vars only include the last intersection point found (Isect).

Methods I've used so far include:

• Finding the first intersection point, then using Copy-X to put it on the clipboard. Then find the second intersection point. Then start Signed Area, using Paste to set the From point, and Vars/Results/Isect to set the To point. This works, but seems a little fiddly.

• Finding the intersection points and, for each, drop to the cmdline and store the first Vars/Results/Isect in A, the second in B. Then Signed Area, and set the points to A and B (by name). Again fiddly.

• Getting rough X values for the intersection points visually (e.g. 1–2), then finding the signed area from the cmdline, with e.g AREA(F1, F2, ISECT(F1, F2, 1), ISECT(F1, F2, 2)). This has the drawback of not showing the area visually, which is a useful teaching feature.

What might be nice would be the ability to set the From and To points by "snapping" the cursor to points of interest, like intersection points.

Alternatively, to store more than just the single last result of a function, e.g. store the last n results, so that you may select from them, or as a list.

Does anyone have any other tips/tricks for this sort of thing?


Anyway, that's just a quibble; what struck me was the wonder of being able to seamlessly switch between different views, Symbolic, Numeric, Plot, Vars, Toolbox, cmdline, and Help, without getting lost, or having to read the paper/PDF manuals, and it all Just Works. That's a fine piece of design, for sure. And that's without even being able to move/access data between Apps, which I've yet to explore.

…

And my daughter is now desperate to get her hands on the Prime

[lrdheat]

I agree, and asked about this very thing several years ago. The CASIO fx-CG50 does a nice job with this sort of thing...

[Carlos295pz]

I also think it can be complicated, but after you get used to using Home as continuous support it ends up being simple, here is my sequence.

[cdmackay]

thanks both for the comments.

Getting from Home, via Menu, that's a nice idea too, thanks!

[cdmackay]

(03-02-2020 04:52 AM)Carlos295pz Wrote:  here is my sequence.

and thanks for taking the time to make that video…

[Carlos295pz]

It gave me laziness to write the steps and that there is the possibility of not being understandable, it is more efficient to make a gif

[cdmackay]

thanks

[jte]

(03-02-2020 12:30 AM)cdmackay Wrote:  ⋮
The Signed Area function is great, which gives the area under one function and above another (or the X-axis) between two points.

However, one thing I thought could be easier, would be a quicker way to select the two end-points as intersection points of the functions.
⋮
Methods I've used so far include:

The earlier versions of the Plot view didn't provide Copy-X capability. I added it as it was a minor change which could give a slight improvement to Signed Area use. (So that one wouldn't have to travel to Home or sneakily do an assignment in Go To etc. to store the ending coordinate for later use.)

I think part of what makes this seem fiddly is that one has to go into Signed Area with a plan already in effect: one must first have (at least) the ending coordinate stored somewhere before beginning Signed Area (so that one can Go To it). (Assuming one wants an ending coordinate that comes from something beyond simple cursoring around.)

Perhaps a way forward is to have Signed Area be an overlay, something more akin to how Tangent (two steps down from Signed Area in Fcn) works. Have some sub-choices in Fcn / Signed Area for

• beginning the process (perhaps picking the "above"),
• for fixing the start point, and
• for fixing the end point (at which point calculation occurs and the overlay is removed).
  

With an interface of this sort, one would choose Fcn / Signed Area / Below F1(X) & / Above F2(X), then move the cursor as one likes using the same interface as when Signed Area is not in use (including using extrema / intersection finding etc.), then select Fcn / Signed Area / Set Start, again move the cursor as desired, and then finally select Fcn / Signed Area / Set End. There are choices with this approach that affect how much the user is railroaded along a certain track (there could be "... / Compute" and "... / Dismiss" choices so that computing multiple signed areas with the same start or end point would be convenient etc.).

(03-02-2020 12:30 AM)cdmackay Wrote:  ⋮
Alternatively, to store more than just the single last result of a function, e.g. store the last n results, so that you may select from them, or as a list.

The most generic approach along these lines would have a new "stack" sort of object added to PPL (perhaps quite like a list, with normal evaluation returning the top item and indexing allowing other items to be retrieved; a setting somewhere could control stack depth for stored results like Isect). (Or, more simply, use lists to store computed results, but this would break existing programs / workflows.)

(03-02-2020 12:30 AM)cdmackay Wrote:  Does anyone have any other tips/tricks for this sort of thing?

I thought you were quite thorough enumerating the possibilities! Nevertheless, Carlos295pz also reminded us that "Get from Home" via the Menu key is yet another possibility.

Writing this, I did wonder about adding anotations to the Paste dialog that would show where each paste item originated.

(03-02-2020 12:30 AM)cdmackay Wrote:  Anyway, that's just a quibble; what struck me was the wonder of being able to seamlessly switch between different views, Symbolic, Numeric, Plot, Vars, Toolbox, cmdline, and Help, without getting lost, or having to read the paper/PDF manuals, and it all Just Works. That's a fine piece of design, for sure. And that's without even being able to move/access data between Apps, which I've yet to explore.
⋮
And my daughter is now desperate to get her hands on the Prime

My daughter enjoyed using her Prime during her last few years in public school (edit: by "public school", I meant grades 10⁠–⁠12; she's in university now). :-)