Circles and Crosses

G. K. Chesterton is fascinated with the imagery of circles and crosses.  He spends some time on the topic in Orthodoxy.  (Incidentally this book convinced me of the need to have a fairy tale focus in the late Casa and early Lower against Dr. Montessori’s advice – I think it is a modern world issue.)

Jeff Dunn posted a Lenten thought over on Internet Monk that deals with the circle and the cross.  We are in a geometry kick right now, so this discussion with some modification lent itself to a elementary lesson.  I commend the “adult” version over at Internet Monk to you as it contains an idea that I removed in the “children’s” version.

 Circle and the Paradox

Materials:     Paper x 2               Drawer of Circles                    Pencil

Purpose:  To provide a thoughtful Lenten lesson to the elementary age child using materials that they know so they will be reminded of it when they use those materials.

The Lesson:

The circle is the basis for most higher mathematics. It led to what we now know as advanced geometry and calculus. From the circle we get the wheel which, along with gears (also circles), puts the world around us in motion. The circle, if drawn properly, is a perfect shape. There are 360 points, or degrees, in your circle, each one equidistant from the center point. If you draw a straight line from the center point to the any point on the circle, you have the radius. A line that goes from one point on the circle to another while passing through the center point is the diameter. The distance around the circle is called the circumference. The ratio of a circle’s circumference to its diameter is measured as pi, an irrational number, meaning its digits never repeat and never end. It short form, pi is equal to 3.14159. Modern computers have been able to measure pi in digits exceeding a trillion without the sequence repeating.

Please choose a circle from the drawer of circles.

This circle will be the only thing on the paper.  Choose where you would like to place the circle carefully.  I’ll give you a minute to ever so carefully trace your circle.


Let’s look at our circle.  The circle is about as perfect of a shape as you will find.

It seems perfectly plausible to make the circle the symbol for the Christian life. Many of us want our Christian lives to be like the circle. We have Jesus as our center, and everything revolves around him. What is wrong with that? We use the Bible as the radius, checking and rechecking verses in the Bible to be sure we are staying in proper orbit around the center, Jesus. Each point in our lives, all 360 of them, must stay in the proper place, otherwise we might become warped in our thinking. Then we will not be able to turn like a circle should. We will be “out of round.” If that happens, get the Bible and find out where we have gone wrong. Our goal is to stay a perfect circle.

Can you make the circle bigger?  Not a circle in your mind.  But the circle on the page.

Give the time for the children to mull this over and provide ideas.  Guide them to the thought that the only way is with an eraser, but that they have worked so hard to carefully trace it.  It seems such a shame.

There is no growth, of course. We can’t make our circle any larger–we would have to deconstruct it first, and that would involve great pain, great stress, incredible turmoil. No, that is not what we want at all. Peace–that’s what a circle is. Perfect and peaceful. Why mess with that?

When something can’t change it is called finite.  The circle is a finite shape.  It cannot grow larger or smaller. Look again at the circle you drew on your paper.   If I took my pencil and added a dot – one point – on the circle do I have a perfect circle any longer?

Give the time to think this through and listed that it would be a slight oval or ellipse.  Hmmm.

Ahh so it won’t be a circle.  In order to make the circle even one degree larger, you will have to recreate the entire circle. You can’t just stick another dot in there and make it larger. A circle is 360 degrees period.

If you want a circle with a larger diameter, you have to start over. Circles may be a perfect shape, but they cannot change. They are stuck being what they are.

Let’s make another drawing on the second piece of paper.  You must listen carefully. This is not going to come from the geometric cabinet.


Draw one vertical line.  What is a vertical line again?

Give the time for the children say that it goes up and down the page.

It doesn’t have to be perfectly straight.  You can make it as long as you want it to be.  What looks like a good length to you?

Now, starting about a third of the way from the top of this line, draw a horizontal line through the vertical line. Make it as large or small as you like.  Do you know what a horizontal line looks like?

Pause and wait for the children to answer or demonstrate.  (The reason for this is so that the child who doesn’t know is given a chance to learn from the group.)

What have you drawn?

Listen to the responses.  Remind the children this is not a shape because it isn’t a closed figure like all the geometric shapes.  Discuss the differences “Wow.  You made yours so much longer on your vertical than your horizontal.”  “I wonder if there is only one exact way to draw a cross?”

Yes this is a cross. A cross is not a perfect shape. Euclid did not use a cross when he developed our modern theories of geometry. It is not perfect in any sense. Just two lines that intersect somewhere.

Yet for the Christian, the cross is where our lives end, and where they begin. You cannot be a Christian without the cross.

And the place where the two lines intersect? That we can call the paradox of Christianity. An intersection of two ideas that don’t go together.  Christian paradoxes are things that our minds can’t understand but faith allows us to know is truth.

God becoming man. Now really–how can the God who created the entire universe shrink himself to become a newborn baby?


God the man suffering and dying. Again, how can that be? How can God, who is the creator of life, succumb to death?


There are many other paradoxes that form the teaching Christians are to follow. To be rich, you must become poor.


To live, you must die.


The weak person is the strongest.


You want to get even with an enemy?

Pause. Love him.

Remember my circle.  Remember how I cannot grow in my circle. It is finite. It cannot be other than what it is.

But look at the cross you drew. Use your pencil and extend one of the lines, any one you like.

While the children are drawing continue.  Draw it to the edge of the paper. Then onto your table, across the floor, out the window, across your lawn to your neighbor’s house. The lines of the cross are infinite. They can go on forever.  They can cross nations and continents and our galaxy into the corners of the universe.


So this day you must choose. Do you live in your safe, perfect circle?

Or do you embrace the cross of paradox?

There is safety and predictability in the circle. And when people look at you, they see symmetry. A circle is nice and neat and tidy. People will look at you and see a good person. The circle is a place where you can have a nice, safe life.

Or do you choose the cross?

Two lines, unevenly drawn, that intersect in paradoxes.


Now before you choose one should think carefully.

The cross challenges you.  There are challenges to what you think is right.


Things are turned upside down from what you think they should be.


You are called to believe when you can’t see. You are told to trust when it doesn’t make sense. And here is the kicker. The cross means your death. It is the death of you being in charge. Death of you controlling what is right and what is wrong. It means you are dead—and the life you now live is Christ Jesus living through you.

Pause.   Pause.

Is our God a tame lion?


No!  He won’t do as you please. He will lead you to places you didn’t think you should go. He will not stay nice and round.  People, especially people  that like neat and tidy lives in their circle, will tell you just how wrong you are to be doing what you do.


The only consolation you have is that you will be walking the way of the cross with Jesus.


And really, what else is there to consider?



Filed under Montessori

3 responses to “Circles and Crosses

  1. This is really fascinating! I wonder, what age were the children that you did this with? Thanks so much for being a part of Celebrating Lent! I look forward to reading more of your blog.

  2. There is certainly a lot of food for thought here! In Googling the references a little further, I came across this related image as well: Flannery O’Connor described the cross as the one Tree with arms wide enough to embrace all the living and roots deep enough to encircle all the dead.

    By the way, we do ask when you join our Lenten link list that you include links to our blogs (Sheila’s and mine) here. Thank you 🙂

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