34 Notes About Math Notes

Gary from MacMost here. Let's take a really close look at what Math Notes can do. 

Now Math Notes is a new feature of macOS Sequoia and it is also in iOS 18 and iPad OS18. The basic idea is you can write out math equations in the Notes App and then see the results. You don't have to calculate it on your own. The Notes App will do it for you. But there is a ton of hidden functionality in there. Let's take a look. 

Let's start by just looking at things that work on the Mac and these will all work on the iPhone and iPad as well. Then at the end we will take a look at things that specifically work with the Touch Screen on the iPhone and iPad. 

First, of course, you can do basic math in Math Notes. All you need to do is type the math equation, use equals, and then use either spacebar or return. So here's an example of what can be done. To do one of these all you need to do is just type something like a number, then plus, another number, and then equals. It will give you the answer there but it won't make the answer complete until you either hit spacebar or return. Then you can see it fills it in. Now it doesn't really matter if you add extra spaces and things. You can put spaces to see things a little clearer, like that, and it will still work just fine. 

Now the first thing I want to show you is that you can use parentheses in Math Notes. So you can set the order of operations by grouping things in parentheses. Look at this first example here. 1+2 are grouped together so they are added together first before being multiplied by 4. You can have lots of different parentheses and nest the parentheses as you need.

Now if you do math work and you write out equations on paper you know that you don't actually write the multiplication symbol. If there are parentheses there you just put the multiplier before it. You can do that in Math Notes as well and it assumes multiplication. 

Now the important thing to realize here is that it doesn't just do the calculation after you type the equation. You can update the numbers and the answer will update. So, for instance, I can change this value here to something else and notice how the answer updates. Also notice that when I select something you get this little control here. Grab this, kind of slider, and change the numbers a little bit. Or you can use these buttons here to actually increase or decrease them one-by-one. 

Now this whole thing takes on a whole new dimension when you realize you can use variables. So you can just type some text, use words like width and height here, and assign values to them. Then you can use them in equations. So, for instance here I can multiply width times height. It takes those values and gives me the results. I can even use them in more than one equation like that. Then when you change a value, like if I were to change this to 5, notice how both equations update. Everything from this point on the width value gets changed and you get new answers. 

Remember I talked about that you don't need multiplication symbols and that even makes more sense with variables. So you can do things like instead of 3 times A you can just say 3A and get the result. This gives you things that look more like what you would write on paper than normally type into a computer prompt. 

Now you can have variables and change them line-by-line. So, for instance, here I start with width and height equal to something. I do a calculation and then the next line I change the value of height and I do the same calculation again. So notice on the third line it calculates 7 times 9. Then I change height to 5 and then on the next line it is 7 times 5.

Now you can also get variable values from other variables. You can do this with two equal symbols on the same line, like this. So here I've got area equals width times height. It is taking it from the values I Just had. Then I put equals again and it gives me the value of area. So, I'm both assigning area and seeing the value of area on the same line. 

Now you can use Special Symbols for things as well. For instance if you don't want to use a slash for division, which is typically how you do it on computers, you can use the division symbol which on US keyboards is Option and Slash. In addition Option and V is the square root symbol on US keyboards. You can actually put that before a number and it will understand it and give you the square root. You can also do this with constants. We'll look at more constants in a minute. So Option P gets you Pi.

Now there are lots of other special symbols and functions you can use. For instance you can use the karat symbol, which on US keyboards is Shift 6.This is for power. So 4 to the 5th power can be written with 4 the karat symbol and then 5. This is typically how you do it in computer programming languages. So you may already be familiar with it. 

But you can also use Functions. Like pow is the standard function for power. It takes 2 parameters in parentheses separated by a comma. So 4 to the 5th can be written as pow (4,5). You can also use special symbols for powers. So you could write 9 squared as 9 squared. So how did I get that 2 symbol there. Well I just typed something, like 8 and then I'm going to use either the fn or Globe key and e, or Control Command Space to bring up the Emoji & Special Character Viewer. Then I'm going to search for the number 2. I can very easily find the 2 here. As a matter of fact I can search for the number 3 and you can see 3, the superscript version of 3. Use that and then equals and it understands what you're trying to do. 

Now you can also do Roots a variety of ways. You can use the standard functions sqrt for square root and cbrt for cube root. But you can also, of course, use the karat symbol to raise to a fractional power like .5 would be a square root, one-half. You can also use the symbol, the Option V like I showed before, to get the square root symbol. There's also a cube root symbol. The way to get that is the same way I showed before, Control Command Space. If you search for Root here you can see there's cube root. Here's some other examples of that and you can combine these to have equations that really look like what you would write out. 

For Factorials you can also the standard exclamation point for those. 

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I mentioned Constants before and you've got a few of them. You've got pi. You can just do p and i. You've got e and just use the letter e and phi you can just use p h i for those.  Now how did I type pi. That's just Option and p like I showed before. For phi I just used the Emoji & Special Character Viewer and searched for that. It comes right up. 

You can do various other functions like Logs using the Log Function. Using ln for natural log. You can use the exp function and log10 as well, if you're familiar with those. 

There's also a full set of Trigonometry Functions. So you've got sin, cosin, tangent. You've got asin, acos, atan. You've got the hyperbolic sins, cosh, tanh as well and they all, of course, work with radiant. So you can see at my first example here I'm actually using a pi constant inside of that function. But if you want to convert from radiants to degrees you can do that as well. So you can use the rad function for that and it will give you the result in degrees. The deg function will convert to radiants. You can see an example of a nesting degree function inside of a cos function. 

Now in addition to doing math you can do unit conversions. So here are a whole bunch of examples. If you just type 4 and in, the abbreviation for inches, it will give you meters. You can type out something, like miles instead of mi and it will give you kilometers. Even understand if you type out miles you want kilometers. Whereas if were to type 5 mi it would actually give you km. Here I'm using 18m and it is going to give me feet and inches as a result. I'm doing feet and inches and it is going to give me a fractional amount of meters. Some examples with areas, with fluid measurements, and weights right here. 

You can also do Time. So you could type sec for seconds and you can see it gives you the results in minutes and seconds. You can add seconds together and you can see in that case it's giving the result as a total number of seconds. Not sure why there's a difference but you can also do hours, minutes, and seconds and it understands that. But interestingly adding hours, minutes, and seconds to hours, minutes, seconds doesn't seem to work. But you can see here you can use in when doing conversions. So 4h for four hours and type the word in and then the unit you want, like seconds, it will actually do the conversion for you. So there is hope for doing much more complex time math if you work with it. 

Math Notes can also handle multiple units. So for instance if you take miles divided by minutes you get miles per minute. If you take miles divided by hours you get miles per hour. It even spells out per. You can do miles per hour, MPH, times the number of hours and get miles out of it and it understands that. Miles per gallon times gallons gives you miles. You can do miles per gallon and it will convert to liters or kilometers. Nice!  

I also note it gets unit symbols like a single quote for feet and a double quote for inches. So you can see it does some math here. You can also use degree symbols. I found that Option 0, Shift Option 8, Option K, and the word deg or degrees all work to find degrees and it will convert to radiants like that. 

You can also do temperature conversions. So it assumes F means Fahrenheit and converts to Celsius. I assumes C means celsius and converts to Fahrenheit. But you can always use in and then one of those, or in this case K for Kelvin to convert to the unit you want. 

You can also put currency symbols in front of numbers and it understands that. So in this first slide here I put a dollar sign in front of these two numbers and it gives me the answer with a dollar sign. I did the same thing with Euros and it worked as well. Yes, it will do conversions. So you can type something like the Euro symbol and 8 and it will convert to US dollars. You can see you can even type out the word Euros and you can use in for something else. So $100 in yen and it will convert to yen. So it is using the same conversion that is in the calculator app for this. Notice the last one I'm actually adding Euros and dollars and since I used Euros first it has actually given me answer in Euros after converting the dollars to Euros. 

It also understands Memory and Storage Units. So you can use things like MB and KB and TB and do math with those. So you can even use that in function there to convert to something else. 

You can also use currency and other units in Variables. So, for instance, here I'm assigning the value of $27 to the variable taxi. $75 to ticket. When I add taxi plus ticket you can see it applies the units there. For the variable distance I have a 15 miles and time is 15 minutes. You can see when I do distance divided by time I get 1 mile per minute or if I add in MPH I get miles per hour. 

The Percentage Symbol also works here. So Instead of having to multiply something by like .01 to get 1 percent you can say one percent. So here I've got two examples of multiplying by percentages to get the result. 

Now back to variables for a minute, you can increment variables by referring to the same variable in definition. So I can do a=1 and then redefine a as a=a+1. You can see here the result I get makes sense. So if I were to change this value to something else, like that, you can see I get the result. So this gives you some interesting possibilities with variables. 

If you're wondering whether you need to all be on one line, they don't. You can use spaces or other dividers like you might want to use a semi-colon to go between things. So here I'm incrementing a variable and getting the answer on the same line which makes it a little clearer on what I'm doing. 

You can use Scientific Notation for numbers with the capital E. So here I've got A=4E10 so it is going to put ten zeros after the four. You can see when I get the result of A that is what it gives me and it uses it in calculations as well.

Here's some functions for rounding. Round goes to the nearest integer. rint is something called banker's rounding which goes to even numbers. So 4.5 goes down to 4 whereas 5.5 goes up to 6. Floor goes always down and ceil goes up to the ceiling. 

There are a lot more functions too. You've got ABS for absolute value. You've got fmod for the remainder of division. You've got the hypotenuse of a right triangle with two parameters. So here, if you have a right triangle that's 3 on one side and 4 on the other the result is 5 for the length of the other side. You've got a min function and a max function but sadly these only seem to work if you've got two numbers in them. You can't do more. You can do Mods or modulus using the percent symbol between two numbers, which typically how I do it on computers but you can also use mod for mod. So this gives you the remainder of division. So 10 divided by 3 you're going to get a remainder of 1. 12 divided by 3 you're going to get a remainder or zero. 

There are also some Bitwise Operations and And and Or using the ampersand or the pipe symbol. These basically take the number, convert them to binary and then either and the ones and zeros or the ones and zeros. Something that programmers might use. 

More? there's definitely more. I explored and tried all sorts of things but I'm sure there's more left to be found. There are even some things I can't quite explain. Like using a tilde symbol between two numbers produces results like this. I can't find any reference for what would produce these results or what the tilde symbol might mean in this case. If you know please let me know in the Comments.

Now there is even more that you can do if you're on an iPhone or an iPad. You can use your finger to touch the screen or on a iPad use an Apple Pencil. So in the Notes App if you write out an equation with your finger or the pencil, like this, it's going to show you that there's an equation there it recognizes and you can tap Solve. It will solve it. Notice how it kinda wrote the number to kind of match my handwriting. It is using a font that is kind of similar to your style of handwriting. I think it has a few to choose from. It will give you the result there. So you can do all sorts of calculations like that and you can see you can check it by looking at what's there and typing Solve. Now the cool thing is you can change the numbers by just tapping on a number. So you can tap on like this number here and then you can move back and forth and you can change the value that's there. You can see the result change. It works really nicely and smoothly. 

So another cool thing you can do on the iPhone and iPad that you can't do on the Mac is you can create Graphs. You would do that by starting with y equals and then use x on the other side. So maybe something like 2x squared plus 3x minus 1. Like that. Then you tap the Equals and then it tells you what it thinks the equation is. So you can confirm that it is right. Then you can type Insert Graph there and it will create this graph and show you the equation graphed out. You can increase its size. You can grab it and move it around in here. You can use two-fingers and pinch it to shrink it but also move it around. So let's get it back here to 0-0 like this. This will update if I change here. So if I go into the equation and I change this number you can see it changes what's there. I can change this number here, even change the power here. With the graph selected you can actually tap the first symbol there at the top in the little menu and you can then change the color, like that. You can even add another equation to this. So let's go and say let's add that and you can see I can add to an existing graph and it will put that line there. Use a different color for that. If I were to tap on the graph there and tap that first little symbol in the menu you can see now I've got the two colors and the two equations. That's really cool functionality and I hope eventually they find a way to bring that to the Mac version of Notes as well. 

So as you can see there's a ton of different stuff that you can do in Math Notes. It's really exciting if you have to do calculations and maybe you don't want to start a whole spreadsheet for just doing a few lines of calculations or you want to combine them with other Notes and text very easily. I know there are going to be a lot of uses for people that work or study science or finance or other subjects as well.