Live: Fun With Math Notes

Hi everyone, this is Gary with MacMost.com.

I'm going to do a live episode today taking a look at MathNotes.

Okay, so MathNotes are not a new feature.

Well, they're kind of new.

They're from last year.

And I'm still geeking out over them because I think they're really cool.

It's a new way to do calculations on your Mac and actually your iPhone and iPad as well.

That doesn't involve going to the calculator or Spotlight or like creating a spreadsheet or anything like that.

You could just type pretty much anywhere you could type text, but in particular in the notes app.

So I'm going to start off there in the notes app.

So here I am in the notes app and I've just got a blank note here.

And let's say I want to do a basic calculation, like adding two numbers together.

I'm going to type 1 plus 1, and then I'm going to type the equals sign.

And you could see the number 2 appears after it.

And you could press return, and it accepts that and puts the number 2 there.

Now, it may be a little hard to see this because the text is usually pretty small in notes.

So I'm going to zoom in so you could see it a little clearer there.

So you could type any expression you want.

Let's say I want to do 5 minus 3.

Then just type equals.

You'll see the answer there.

And you can press return.

And it kind of puts the answer there and puts the cursor afterwards.

So you could do lots of different basic calculations like this.

There's addition and subtraction, of course.

But let's also take a look at, say, multiplication.

So you want to do 5.

And in computers, traditionally use the asterisk for multiplication.

If you've ever done any programming, you know this, but you may not have done any programming.

So maybe you don't know that.

So on the US keyboard, just shift eight.

But on other keyboards, asterisk at the asterisk character somewhere else.

So you type asterisk and then say seven and then equals.

And you could see you get multiplication.

It even will change that little asterisk to an X there or the multiplication symbol.

It's not really an X.

It's more of a straightforward squared off cross.

But you could also actually use the X key on your keyboard if it's in the right context.

So 4X and then 9 equals, and you could see converted the little X character to multiplication and you get that.

Now for division, you could do something like nine, and then it's the slash, which kind of mimics like a fraction kind of, and that's how you do it in computer typing.

So nine divided by three equals three, and then return, and you get a division result there.

So you could do all sorts of basic calculations, but you can go like way beyond just two numbers, right? So if you need to like, say, add up a bunch of stuff, you do 25 plus 76 plus 321 plus 6 plus 48, you know, and just keep going, even maybe subtracting something minus seven.

You know, you're doing some sort of calculation and it's nice because you could see it all here.

It's not like in a calculator where you're doing one number at a time, although the new calculator, you can actually type it out kind of like this.

But now when I do equals, it puts it all together like that, which is really nice.

and you can make changes.

So if you look at this and say, oh, this isn't supposed to be 321.

This is supposed to be 312.

You can change it and the result will change to match that.

So the calculation isn't done just when you type equals, but once you've set this up, now you can further refine the calculation.

Now, if you do some math, you know that order of operations is kind of like an important thing.

So for instance, if I wanted to do 2 plus 3 or 2 plus 3 times 9 equals, I get of course 29.

It's doing the 3 times 9 first and then adding the 2.

But if what you really want to do is add 2 plus 3 and multiply by 9, you would use parentheses.

and this works with parentheses.

Two plus three times nine equals and there you get the answer that you're actually after and you can have a whole bunch of nested parentheses used with multiplication, division, addition, subtraction and all of that to get the answer you want.

So, you know, you can do more complex things like that and you'll get the right answer.

So that's really handy to be able to go ahead and do it like this.

Now, we've looked at the basic math functions here, but let's take a look at some extra ones.

Like, for instance, if you want to square something or cube something or, you know, take something up to a power, you can do, say, 5 squared.

You would use the caret symbol.

That's on US keyboards, shift 6 and 5 squared equals 25.

And this is basically raised to the power.

So if you want to do cubed, you would change to three like that.

If you want to do square root, well, as math people know, that square root is, you know, raised to the power of a half.

And so you could do it like that.

So that's how you do that.

There are other symbols as well.

For instance, a factorial is exclamation point.

So you can do five factorial if you have use for that.

There are other things, percentage.

If you do, say, 5%, you would know, like as a math nerd like me, you would know that they equivalent to 0.05.

And if I do equals, it actually shows you that.

So you could type out things like, say, if you've got a bill that is 6752 and you want to find out what, say, 21% of that is, you could multiply by 0.21 and get your answer.

But you could also multiply by 21%.

It recognizes the percent symbol and changes this to 0.21.

So percent symbol works.

And there are other things that work as well, which I'll point out as we go along.

If you do want to use divide instead of slash, so I do like 12 divided by 4 equals 3, and you're like, oh, I hate the slash.

Option D, actually, it's shift.

I thought it was shift option.

Oh, it's option and then slash.

That's what it is.

Option slash gives you a division symbol.

Makes sense.

So it's had a slash, option, slash, and it understands the division symbol.

So it'll give you a nice division there and it will look nicer for you.

Also, if you want to do square root, you can do option V like that.

And you could do say the square root of nine like this.

If you want something more complex, you might have to do like parentheses like that.

And you can see how it takes care of that.

So that's really cool to know.

So you've seen how you can do math.

You see how you can change the numbers after you've got the formula already typed.

But what's really cool is that you could do this in places besides notes so far so uh i can go here to say text edit let me uh create a new text document move it over i'm in text edit i'm typing uh some text and i can actually do the same thing four plus five equals and there it puts the answer so just equals and then you know kind of return you can do 7 plus 2 times 5 equals there's your 45 so you can do this kind of thing not just here in text edit but here i am in pages and you know 6 times 6 equals 36 um here i am in mail just to give you an idea of like why you might want to do something like this in mail here's like a message which I'm sending, by seeing an order for 15 packages of widgets.

And you want to make sure you get the right number.

So you're saying each package is 12 widgets, right? So I need a total of, and instead of doing the math in your head or just putting it there, maybe with the calculation, you can do a 15 times 12 equals, and it does the math for you.

So not only did it do the math, but you could see here, it includes the entire result, allowing you to easily clarify something in an email message.

And this is a simple multiplication, but imagine something much more complex, like calculating lumber prices per yard and with lots of other things in there.

You could have calculations in your mail message as you go along to prevent mistakes in communication.

Let's go back to notes now, and let's look at some stuff that actually only works in notes.

So you can use variables.

So variables, if you're not a programmer, is having the, it's having basically a little storage place where you can store a number temporarily.

So you can, for instance, have two numbers and want to add them together, instead of just adding the numbers together, you can store each number in a variable and then add the two variables together and get a result.

So this allows you to kind of like memory on a calculator, except you can have as many of them as you want.

So you can store results or values in variables.

And the variables can have names that can be meaningful to help you understand calculations.

So for instance, let's take a look here at, if I want to create a simple variable called a, I could do a equals, and I can give it a number like seven.

And then I could do b equals, and I'll give it a number like five.

And now I could do, oh, a plus b equals, and you could see how it figures out that this is a variable and this is a variable so that it's actually doing the calculation from those two variables.

And you could change the value of the variable and the result will change.

So you do something more meaningful.

Like if you're measuring your yard, you can do yard width equals 27 and yard height equals 56.

Right.

And then you can do, say yard width times yard height, and it would help if I didn't have a spelling mistake, equals, and you can see it gives that meaningful answer there, and you can look at this line and tell exactly what's going on.

You can even have some other text in here, so you could have variables defined kind of at the beginning of your note and then you know the order of operations it happens as it goes down so yard width yard height and there we go if i want to say well what happens if the yard uh width if i include my neighbor um yard width equals uh 55 and then i want to you have this same calculation here so you can see here as it takes the value yard width yard height it gives you the result then you're changing yard width and then it's giving you a new result from the same thing so you can do some really cool stuff with variables and variables can be used just like numbers so you can include them in parentheses and everything like that and you can change the values also notice sometimes that when I look at a value like this if I select it I get this little button here, I can click it and I got a slider and I can actually change the value by sliding.

You can see how it changes there.

I can even select this value here and change that.

It's just tricky to bring it up.

There we go.

And now it's going to change the results for both of these calculations like that so that's kind of neat for you to be able to do things like that um so yeah there's lots of cool stuff you can do with variables and you can store results and variables so i could do like this yard area equals and then i could just have yard area height equals and I get the result there like that.

So now it's kind of clear what it is I'm referring to.

I'm not just saying yard width times yard height.

I'm saying, yeah, this is the yard area because I do all the calculation here and assign it into a variable.

So lots of cool stuff that you can do.

And I also want to point out that, you know, you can use variables in kind of a very algebra-like way.

So I can do a equals 8 like that, and I can do 5a equals, and you can see how it implies the multiplication here.

So implied multiplication is all part of this.

So you can do like 5 parenthesis 6 plus 7 equals, and it implies the multiplication, which is just a really very important part of doing like algebraic equations and stuff.

Not to always have to put a dot or multiplication symbol there all the time.

Let's take a look at functions because you could do functions as well.

I've just shown basic math now, but let's say you want to get the sign of a number, like sign of 0.5.

You could just do a function like that.

If you've ever done programming, you probably recognize functions that look like this and have like three or more letters that abbreviate it but this will calculate the sine uh this will calculate say the cosine like that and um you can even do units in here like so this is 0.5 because when you do math functions uh trigonometry functions on computers it always assumes radians but if you want degrees you could do 90 degrees like that and it will understand the answer oh i think it's just D-E-G.

Yeah, there it goes.

But you could also do the symbol, which is option shift 8.

Yeah, option shift 8 gives you a degree symbol.

Yeah, and that does it.

So the cosine of 45 degrees is like that.

So there's another symbol that works.

I think you could even do like 5 minutes 22 seconds and see if that works.

So, no, maybe not.

I think it actually does work, but it's converting from the straight quotes.

Let's try to force it to not convert.

Nope, it's not going to do it.

I thought that it would do minutes and seconds, but it doesn't seem to want to.

so um we've got that we've got tons of other things you can do a deg and uh do conversions to radians or do uh you know radians and a conversion degrees uh you can do sine cosine tangent uh you could do you know put an a in front of it for arc sine arc cosine arc tangent put an H after it for hyperbolic sign.

Now what this is, sign, hyper, I forget what that is.

It's been too long since I've taken trigonometry.

So you can do all those kinds of things.

You can also do unit conversions.

So the idea here is with unit conversions, you would convert, you know, you want to convert like feet to meters, that kind of thing.

So it's going to understand the commonly accepted symbols for those things.

Like, for instance, if I were to do 6 and let's say FT for feet, it assumes, okay, feet probably going to meters, right? If I do inches, meters again.

If I combine and say 6 feet, 4 inches, it understands that.

If I do eight meters, then you could see it converts to feet and then inches.

But you can also do math.

So six meters plus three meters equals.

And it's going to assume you don't want a conversion there.

I believe you can do as feet.

There you go.

So it understands as and then another thing after that.

And so now you've got that.

Now you can actually change this.

You can see how it changes there.

So you could do stuff.

You've got, you know, seven gallons to liters.

You could do 67 kilometers, converge to miles, stuff like that.

Eight ounces.

Now, OZ, right, there we go, kilograms.

So you've got stuff like that.

It even understands time.

So you could do like, say, 15 days.

We'll convert that to weeks or 15 hours.

Convert that to days.

You can do H like that.

It's like 15 hours, 23 minutes, 56 seconds equals.

And it gives you that there.

So I think you can do math on this.

plus let's say I don't know 56 minutes is it going to give me no it's not going to do it oh I think maybe maybe if I do minutes just by itself it will do it because it's probably confused the minutes is probably yeah so the minutes I bet you because by itself it just thought it was meters.

But I think you can do like, let's say five hours, six minutes plus 20 minutes equals.

Ah, there we go.

So you could see it could do calculations based on durations, which is really neat.

And it could do multiple units and use them in calculations.

So if you say we traveled 140 miles and we used six gallons of gas it converts it to miles per gallon or we traveled 100 kilometers in an hour to one hour a better calculation would be like 0.78 hours and you could see oh so you're traveling this speed right that many kilometers per hour so you can see it it does that um so it does really good with that kind of thing um combining units and stuff uh and let me go and take a second here to go back into other apps uh mail text edit pages i'll just have a trait in text edit and let's talk about some of the stuff I've talked about, it's not going to all work here in other places.

It seems that you can only do one expression at a time.

So if I do a equals six, b equals seven, a plus b equals, it doesn't get it.

It's not doing variables and it's not doing multiple expressions.

So you'd be able to do lots of things like six meters equals there, as long as it's just one expression it only seems that in notes you can do multiple expressions so it's important to note that let's take a look at working now with doing stuff that converts things but you can do currency conversion i showed you unit conversion let's do currency conversion and this only works in notes.

You can't do it in other apps, I think.

Let's give it a try in both and see.

So if I were to go and say 75 Euromus, it converts it to dollars.

And this is different than what it was doing before.

So a conversion like, say, 67 degrees Fahrenheit, which you can do with F, it converts to Celsius.

That's a hard-coded conversion, right? How you do that isn't going to change this change is based on the current exchange rates so this is a much different kind of conversion kind of thing you can do this and you can um combine units so and you can use symbols too so i can do 75 dollars plus and then i could do 56 oh i think it's trying to remember what the symbol for euro is but if you could type the symbol for euro you can do it otherwise it's going I could just use the word euro there.

And you could see it's doing the conversion like that.

And I believe it's taking the first thing.

I'll do plus $7.

So you could see it's doing euros.

That's the symbol I was looking for.

I don't remember how to type it just off the top of my head.

So yeah, you can do currency conversions, but those are not going to work here, I believe.

Yeah.

So when you're doing math notes in other apps besides the notes app, you're limited to basically a single expression at a time, which still makes it very useful.

We saw my example in mail before, and you can't do things like the currency conversions, which are more complex.

So the full math notes, that's in the notes app, but you get kind of a simplified version of it in other places where you type text on your Mac.

So let's also take a look at another place where you'll find this, which is in the Notes app, but not the Notes app on your Mac, but the Notes app in the iOS or iPadOS version.

This is my iPhone here.

And what I'm going to do is I can do all the same stuff here.

I could type and all of that, but I can also draw, and I've switched into drawing mode here.

If I type basically here, there we go.

You do four minus six and equals, and there you can see, negative two.

But if I switch to the mode here, let me go and use the pointer device.

There we go.

I'll use my mouse to show here through accessibility functions.

And I'm going to draw instead.

And this is really cool.

So this works in the iPhone with your finger, which is the iPad with your finger, and works on the iPad with the Apple Pencil, which is really cool.

And I could do numbers like this.

Now, drawing already is not something I'm good at, but it's worse when you're trying to do a mouse on a screen delay and draw.

So, yeah, this has got to be crappy.

But there we go.

If I do that, you could see it gives me the little calculation there, and then I can select solve and actually put it up there.

And it even does it in kind of a handwriting style.

I think there's a bunch of little handwriting styles it has, and it figures out which one matches yours closest.

So you can do all this by drawing.

And it's really cool if you have an Apple Pencil on an iPad, you could just write down a lot of math equations, even using variables and stuff, and you could do it all by drawing.

So that's cool.

But what's even cooler is there's an extra function that works on the iPhone and iPad that graphs.

So to graph something, you need an X and a Y value as part of an equation.

So I'm going to do that here by drawing, let's see y equals that's how you typically have an equation here so i'll do y equals uh 2 x plus let's say 3 and i'm even going to make the x squared to make something more interesting now to actually get this to work, I tap on the equal sign and I could, you know, copy the expression.

I could see it here.

I could insert graph and I get this cool little graph here and I could drag it to make it larger and move around and move it around in the note.

Um, and there are other things you can do, uh, in here.

Oops, I made it go away.

Um, insert graph like that.

Unfortunately, this isn't on the, uh the mac version of this doesn't even show up when you view this note over iCloud or i think maybe it does um let's go switch back to the notes app here and then here is that note where i've typed all this stuff so yeah it kind of appears i mean it's trying to appear but not as elegant right um you could see what i drew and all that on the iPhone version, right? So yeah, it's really cool to be able to draw those graphs and you can then change like the numbers in the graph and stuff like that.

That's really fun to play around with.

And I hope that comes to Mac one day.

So I'm gonna take a look and see if there are any questions here before I move on.

yeah i would have loved to have this when i was in school too as a matter of fact oh you know this just makes me think of education all the time uh in terms of the usage because like we look here let's go back uh to here i've gotten this thing this is like a typical thing that is just so cool.

You could do notes that are like this.

Math problems and remember notes, you can collapse sections.

So you can have a whole bunch of these where you have variable names to make things really clear.

And the idea is here is, you know, you can have some text like how to calculate the amount of liquid that can fit into a tank.

So you can add lots of text.

You've got your tank radius, tank height.

Then you do it in steps.

Tank volume equals.

And oh yeah, look, pi.

You can actually type pi by using, I think it's option P.

Yeah, option P.

So you have to type 3.14.

You can actually type the value pi, the symbol pi.

And then times tank radius to the second power squared times tank height.

That's tank volume.

And then you could view tank volume there.

And it gives you the result in meters cubed.

And then you could say tank volume as gallons equals.

And then you get the conversion to not only a liquid measurement, but, you know, an empirical liquid measurement there.

And you could understand how each one of these works.

And you could add more text here about, you know, something about, you know, the volume versus the amount of liquid that could be in it or the units that are being used or just helping you understand that.

And then, you know, you could just fill this note up with all sorts of calculations like this.

Just building this yourself when studying for, say, a math test to try to figure out all these things could really be helpful in helping you understand it.

But also, you could have much more complex things that help you in business, like if you always deal, say, with lumber or plumbing or something where there's measurements and you're always calculating volumes and stuff like that.

You know, you can create little math, you know, programs like this and sure they could be done in spreadsheets, but I like them being done here.

You know, because you could spell things out and put text into them and have good variable names and then go back and edit them later.

And yes, you can go back here and change the amounts here.

And remember I had that thing where it was, you know, there was another volume here, you know, another like change.

So I could change the tank radius, you know, and say, you know, if the tank was just a little larger, you know, and then I could put, you know, tank radius equals and give it 21 meters and then do the calculations again and you can kind of follow along it's really uh just a cool way to do it without getting bogged down into actually like doing this calculation each time and figuring out like oh let's let's go ahead and change let's go make the tank just a little bit large larger height doesn't seem to change it that much but let's change the radius and that really pushes it up so it's like oh changing the radius because of how the calculation works actually increases the volume a lot more than just making the tank a little taller things like that there's all sorts of cool things that you can do um and uh it's fun to play around with and you don't have to do it as its own note you can have a note that's about something completely different and then just have a calculation in the middle of that note and the same thing in a pages document uh you know even though you can only do one per line or you know one expression at a time kind of thing but you still can have calculations like this.

It's so handy, and I encourage you to play around with it and just think about other uses for it.

So, you know, thanks for watching.

I do want to remind people that if they like the videos I make and find them valuable, to just check out my Patreon.

And, you know, you can just go to this URL and just read about it and see what it is you get and how it supports MacMost, how there are no ads at MacMost.com or in the newsletter, for instance, ad-free, sponsor-free and everything like that because of my Patreon supporters.

So check that out.

And I hope you found this useful.

Thanks for watching.