Category Archives: Mathematics

How to Print to PDF on your iPhone or iPad

This how-to is based on iOS 10 and I only just discovered this feature, in spite of having looked for it many times over.

Whether from a website or from a word processing app or just about anywhere, I’ve always wanted to be able to print to PDF on my iOS devices. It seemed only natural that Apple would make something like this available when you print from your device. When you go to the share icon and choose to print, shouldn’t one of your options be to select a PDF printer? But, alas, you can only select an AirPrint enabled printer on your network.

Well, I have GOOD NEWS! The capability is there and has been there all along.

Here’s what you do:

  1. Go to any app that is print-enabled and select to print. Usually, that means finding the share icon.
  2. In the extensions menu, tap Print:
  3. Now, for the secret sauce. In the print preview window, use two fingers to expand the page (opposite of “pinch”). In other words, touch the screen with two fingers and spread them apart. VOILA!!
  4. You now have a preview of the PDF that you can send to any other app, including cloud storage such as Dropbox, Google Drive, iCloud, or OneDrive. You can even send it to apps that allow annotations on PDFs for marking up.

Some other helpful related tips:

  • Some apps like the Microsoft office suite of apps have the print functionality embedded somewhere besides the share icon, so you may have to look for it.
  • The Word app, at the time of this writing, does not have an export-to-pdf feature so this is extremely useful if you want to produce a pdf of your word documents.
  • Occasionally, the print preview is blank and I cannot expand the preview window. In that case, I just cancel out and try again. It usually works the second time.
  • Articles in Safari work best if you first switch to reading mode before you select print. To do this, tap the reading mode icon at the left end of the address bar:

Hope this was helpful!

Is it a core requirement or just an elective?

This week of Creation Care emphasis has coincided with a very busy time of the semester on the Plainview campus.  We are in the first week of early registration for the Spring term which means faculty and students alike are pouring over course schedules and degree plans.  As a result, my mind has unavoidably conflated the two.  As I listened to Rachel Lamb’s message in chapel on Wednesday, I was challenged in a new way regarding the role of Creation Care in my daily walk with Christ.

It was several years ago when we first began our Creation Care emphasis week at Wayland that I first made the connection between caring for the environment and my duty as a Christian to be a steward of God’s creation.  Prior to that moment, I knew I was responsible to God for managing my own resources in a way that honors Him, but I had not recognized God’s creation, the physical world, as my responsibility.  It became obvious to me through meditating on the Psalms that God’s handiwork is all around, and how I live my life not only has an impact on the people around me but on the physical world as well. So, I have taken small steps to lessen that impact and even engage in creation care as worship of the Creator.

And yet, I have not been as persistent or committed as I ought. That’s what struck me in chapel on Wednesday. Rachel presented a three pronged approach to serving our Lord by serving his Church, serving people, and serving creation.  From what I heard, she went one step further and claimed that all three were necessary.  You cannot eliminate any one of those.

It dawned on me that I often treat my responsibilities to God, including service, worship, study, even stewardship of his creation, as if they were “electives” instead of “core requirements” in my daily walk.  As we schedule our classes for next semester, we make sure to first include the ones that are required and then pick and choose our electives based on what fits our schedule and interests.

My challenge to you (and especially to me) is to “enroll” in the core requirements of our relationship with God. Time with God is not an elective.  The study of his Word is not an elective.  The stewardship of his creation is not an elective, especially when neglecting and even wasting his gifts has a demonstrably harmful effect on the “least of these.”  Consider for yourself what are the core requirements of your faith and bring them back into focus in your daily walk.

When I consider your heavens,
the work of your fingers,
the moon and the stars,
which you have set in place,
what is mankind that you are mindful of them,human beings that you care for them?
You have made them a little lower than the angels
and crowned them with glory and honor.
You made them rulers over the works of your hands;
you put everything under their feet:
all flocks and herds,
and the animals of the wild,
the birds in the sky,
and the fish in the sea,
all that swim the paths of the seas.
Psalm 8:3-8

Moving OneNote Notebook to OneDrive

I was asked a great question in class today. Someone had a friend whose computer crashed and the student was worried about what would happen if that wiped out an important OneNote Notebook. That would be a catastrophe for me, if I were to completely lose either my Wayland or even Personal Notebook from OneNote.

Fortunately, that’s not going to happen since I actually have both those notebooks in the cloud and are thus, synced across several devices. Even if an electromagnetic pulse (EMP) knocked out all of Plainview, my notebooks are stored safely on servers in Microsoft’s data farm. I should be careful to say it’s not impossible, just extremely improbable.

So, how do you move your notebook to OneDrive? Assuming you have an Office365 account, which all faculty and students at WBU have access to, you first need to log into your Office365 account. To do this click on the File Tab, then click on the Account Panel. From there, click Sign In and log into your account.

Next, open the Info panel File tab in OneNote, click the Settings dropdown next to your notebook (in the Info panel) and click “Share or Move”


Then, make sure you’re using the correct Office365 account, click Continue, and voila!

You can also share your notebooks using the Share panel and send links or invite people to edit your notebooks.

It’s okay to feel inferior


Brick Wall
Find value in being the wall, when alone, you are only a brick

Not all posts on this site will have to do with math, teaching, or technology.  For example, today, during my time alone with God, I was impressed to record the following in my journal.  It may not be exceedingly profound, but I don’t want to soon forget it because I am often, easily wounded when my ego takes a hit.

Do not let your feelings push you to overreact when you encounter someone that excels at something you do not. For one, you must remember that your value, whether to yourself, to the world as a whole, or to your creator, does not depend on how well you fair against other individuals. You are vastly more complicated and intricate than just one trait or skill. Even though it is easy to fall into the trap of assigning general superiority to someone who has bested you or overshadowed you, remember that there is a uniqueness to your make-up and that uniqueness allows you to meet the needs of others in vital way. I think it is also worth remembering that the value of single brick in a wall is not in its uniqueness. It may even be the case that removing one brick will not bring down the wall. Even so, you are part of something larger. You together with many other bricks hold up your portion of the building. The wall needs bricks. It may not need each and every single brick, but that’s not important to the bricks or the wall. The wall needs to be a wall, it needs the parts in order to be the whole. Find value in being the wall, when alone, you are only a brick.

Cheryl’s Birthday – Singapore Math Problem

This math problem went viral yesterday so I had my kids tackle it. It took us all working together but we got a solution.

Here’s the problem that appeared all over reddit, Facebook, and Twitter:


Don’t read any further unless you want to know the answer. #spoilers

Hint 1: Albert’s first statement rules out any month with a unique day (18 or 19) since he’s certain Bernard doesn’t know the exact date. If Bernard had been told 18, for example, that means he could know it was June 18, but Albert is certain Bernard doesn’t know so it couldn’t have been June that Albert was told. Same goes for May since the 19th is unique to May. 

Hint 2: With May and June ruled out, Bernard says he now knows what the full date is. So the day couldn’t have been one that is in multiple months (i.e., 14 is in July and August). So, the 14’s are ruled out. 

Final Hint (aka the solution): Since Albert finally says that he knows the date and we’ve ruled out May, June, and the 14th’s, we know it has to be a month with only one date left, namely July 16. Since August still has two choices, the 15th and 17th, Albert wouldn’t have been certain that he knew the date if he had been told August. So Albert must have been told July. 

Final answer: July 16 is Cheryl’s birthday. 

The Mathematics of Love

With Valentine’s Day around the corner, the whole of humanity is looking for answers on how to be truly happy in love, right?  And, certainly everyone is thinking of using the most powerful tool ever devised for answering life’s most difficult questions:

Mathematics, of course

Thanks to Hannah Fry’s TED talk posted today, we learn that Mathematics actually has a lot to say about optimizing your chances of finding love.  I’ve always been a big fan of hers, following her on Twitter (@FryRsquared), but this was an especially interesting talk.

In honor of Valentine’s day, check out the “Mathematics of Love”

Connect the Dots Like a Numerical Analyst

I have to say, teaching Numerical Analysis is one of the highlights of my job. Granted, my primary responsibility at Wayland is the Virtual Campus Director, and I will never teach Numerical Analysis online. Nevertheless, I LOVE it. In fact, the course banner that I use in Blackboard reinforces that fact to my students every time they log in:

Just as a for instance, I was able to get them to “solve” the age-old Connect-the-Dot problem. What is that, you ask? Well, simple: We all know, from the time we are toddlers, how to complete a Connect the Dot worksheet:

BUT, what is the mathematical solution? After all, math majors should look at the connect-the-dot worksheet and wonder, “What’s the equation of the solution?”

So today, as an introduction to using splines for interpolation, we derived the simple formulas for a piecewise linear interpolant:

Given a set of n+1 points with coordinates {(x_j, y_j)}_{j=0}^n, we can uniquely describe the piecewise linear function S(x) where S(x_i)=y_i for all i=0, 1, ldots, n, as follows:

S(x)=Big{ S_j(x),   xin[x_j,x_{j+1}]   , for j=0, 1, ldots, n-1

where S_j(x)=a_j x+b_j,

a_j = displaystyle frac{y_{j+1}-y_j}{x_{j+1}-x_j},

And b_j = y_j - a_j x_j for j=0, 1, ldots, n-1

At least, that’s the solution I told them in class today.  The truth is that’s not correct.  In fact, this will only “solve” the limited case where you always move left to right and never go back the other way.  What we really need is a parametric approach.  Given the initial data set above, we assign a parameter t in mathbb{R} to each point, say t=j for the point (x_j, y_j).  Then we have the following solution to the Connect-the-Dot problem:

Given a set of n+1 points with coordinates {(x_j, y_j)}_{j=0}^n, we can uniquely describe the piecewise linear parametric function bar{S}(t) where bar{S}(j)=(x_j,y_j) for all j=0, 1, ldots, n-1, as follows:

bar{S}(t) = Big{ biglangle S_{j,x}(t), S_{j,y}(t) bigrangle, for j=0, 1, ldots, n-1

where S_{j,x}(t)=a_{j,x} t+b_{j,x} and S_{j,y}(t)=a_{j,y} t+b_{j,y}

a_{j,x} = x_{j+1}-x_j and a_{j,y} = y_{j+1}-y_j

b_{j,x} = x_j - a_{j,x} t and b_{j,y} = y_j - a_{j,y} t for j=0, 1, ldots, n-1

That’s better, don’t you think?  From there we launched into a derivation of linear system approach to interpolation by natural cubic splines.  Then I ran out of time before finishing the derivation, which lead to the instagram post below…

That moment when class is over but you haven’t finished the proof… #mathteacherproblems

A photo posted by Scott Franklin (@splineguy) on


The Importance of Your Worldview

This week, I have the privilege and honor to lead the discussion in the Faith and Science course at Wayland.  The topic of discussion will be the importance of your worldview.  We start with a discussion on the 19th century masterpiece, “Flatland: A Romance of Many Dimensions” by Edwin A. Abbot.

Then we’ll discuss a couple of readings:

Are Scientists Biased by Their Worldview

The Importance of Worldview

Slides for guided discussion:

18 Basic Tips and Tricks for the Teacher’s iPad

The best thing you can do to familiarize yourself with the iPad is just to play with it.  You’ve got to be willing to explore by tapping, pinching, and swiping away.  One of the core design principles at Apple has been that their systems should be intuitive.  As you learn some of the basic interactions, you simply need to explore these common icons and gestures in different apps. Below are some the most basic tips and tricks that help teachers (and most general users, as well) to navigate their iPad.

1. Launching and closing apps

When you are on the Home Screen, you can simply tap on an app’s icon to launch the app on the device.  Once an app is launched, all you need to do to exit the app is click the home button at the bottom of your device: Apps don’t completely close down when you move to the home screen.  They also don’t “run” in the background unless you have Background App Refresh enabled for the app.  An app will save its state and you can return to the app later. To completely close an app, double tap the home button and then swipe across to find the app you want to close.  To close the app, swipe the app up and away.


Continue reading 18 Basic Tips and Tricks for the Teacher’s iPad