Circles, Triangles & Holes

Wait a minute!  We have shared marble stories with you about playing in circles and with holes, but “triangles”? Did you play marbles as a child or do you still play?   Bet you played in circles.  Have you ever considered how children in different countries (or even on different continents) set up for a game of marbles? Look at our lead stereoscope image carefully. This group of five boys have drawn a large circle in the dirt.

We think that the shooter is “knuckled down” at the edge of the ring where the other child is pointing. The pointer seems to be a referee of sorts. But why is a second boy inside the ring and what is he doing there? He can’t be shooting can he? If he is picking up his winnings, then he should be outside the ring. Right?

Circles, Triangles, & Holes^[1]

Our question is this: “Who taught these children, and others world-wide, to draw a ring and shoot marbles from the outer edge of the ring?” Were they ever taught to shoot? Did someone have to teach them how to do it, or could they develop the game spontaneously and independently?^[2]

Does the way children set up for a game of marbles depend on the culture in which they were raised or the one in which they live? Does the way they set up depend entirely on their observation of others at play or on how others taught them?

Child’s Play

What prompted us to start thinking about these questions and others is a digital image: “This image of French boys shooting marbles was taken in the 1930s. The boys look to be on their way home from school. Note how they are wearing school smocks and berets. Also notice the triangle they are shooting in rather than a circle.”^[3] While we found the boys smocks arresting, it was the triangle which they drew in the dirt to shoot into that really caught our attention.

Regrettably, we have been unable to find a digital image, historical or otherwise, of children playing marbles with a triangle which we can use in this post. Should we find one later after publication then we will return to this post and add it. If you have such a photograph which we may use then please contact us and let us know about it!

We will return to this idea of a triangle marble game in a bit. First, we wanted to learn a more about at what ages children learn their shapes.

Baby Talk

We used the Bing browser to help us answer at least some of our questions about children learning their shapes and drawing them. “According to the web search results, a circle is easier for a child to draw than a triangle. This is because children typically learn how to draw circles before they learn how to draw triangles.

Another source states that children can copy circles by the age of four, but they may not be able to copy triangles until the age of five. Therefore, drawing a circle requires less fine motor and visual skills than drawing a triangle.”^[4]

Ok. This sounds promising. This supports the idea that children can and do learn circles before triangles. “Children typically learn how to draw circles before they learn how to draw triangles. One source states that three year olds are able to make basic circles, but they may not be able to draw well-formed squares or triangles.^[5]

Space & Shape

Yes, this is a start to understanding at what age children learn basic shapes. But look at this photograph of an antique shagreen (almost certainly sharkskin) bag with spilled antique marbles. Do you see circles? What about a rough triangular shape? Notice something else? The shapes are dimensional and not flat like the shapes a child learns to draw. Yes, there are “flat” shapes, like the ring a child draws on the ground. But a circle can also be dimensional like the holes some children and adults dig when playing marbles.

This gentleman in Eufaula, Oklahoma, for example, has combined space and shape in this marble game in which players shoot marbles hole to hole.^[6]

“Although children accurately perceive shape and space in their everyday environments, preschool children from about three to five years of age need to learn to think about these topics. Our main educational goal should be to promote understanding of basic geometry.”^[7]

Deceptive Complexity

Well, no wonder we wondered about how and when children learn to draw circles, triangles, and holes in order to play marbles. The question sounds simple. It looks so simple. But it is complex. We are only really considering two “flat” dimensions: triangles and circles. A hole, as illustrated above, is a dimensional circle. This is very obvious in the photograph.

But consider this: a circle has diameter, chord, radius, arc and tangent.^[8] And some children have drawn a circle within a circle to play. We have never seen children playing in a ring in which the ring or circle intersects another circle.

And a triangle is never just a triangle. “If none of the sides of a triangle are equal (of equal length), the triangle is scalene. If two or more of the triangles sides are equal, the triangle is isosceles. If all three of the sides of a triangle are equal, it is equilateral.”^[9]

Let’s Regroup and Review

“In preschool, children can learn to identify and name circles, triangles, squares, rectangles, and ovals. By using materials such as posters, blocks, books, and games, teachers expose children to various shapes and help them analyze two- and three-dimensional shapes in various sizes and orientations.”^[10]

“Many children are ready to begin learning about shapes and colors when they are 18 months although each child is different. Some may be ready a little sooner and some may be ready to learn when they are closer to 2 years old. By the time your child is three, they may be able to identify basic shapes such as circles, triangles, and squares and are able to recognize multiple colors. … Shape and color recognition are an important part of developing your child’s critical thinking skills and helps to give them language to categorize and describe the world around them.”^[11]

But you have to consider that millions of children worldwide and across generations had no schooling.  Instead they worked alongside adults in mills and tanneries, onboard ships, and on family farms.  And they served in armies and navies around the globe.

Ready to “Play”?

You may find some recommendations in social media and in relevant literature to allow children as young as three to start playing with marbles under supervision. Remember the ideas about space and shape; children need all kinds of lessons and stimulation in order to learn about shapes, size, and dimension. Caveat: Children three years old still put things in their mouths !

And playing with marbles is not the same as playing an unsupervised marble game with others.  “The circle is a universal symbol that can represent almost anything and also relates to Piaget’s theory of increased symbolic thought, the child is making their first symbol or first conscious representational attempt.”^[14] Circles, after all, are needed by a child to draw a human head, apples, oranges, balloons, and so on

We are confident that by the age of six a child should be able to play marble games with others and with little or no supervision. Remember Matthew Wills supports the idea of children setting up and then playing a game of marbles spontaneously and independently. We do too. But it is obvious by now that in order play marbles impulsively a child must have learned a good deal about shape, size, and relative dimension.

Back for More Marble Games

We really like this Lithograph by Alexandre Decamps who was born in Paris in 1803 and who died after being thrown from a horse while hunting in 1860. Decamps traveled in the Middle East when he was young and, at least partly because of his travels, he became “…one of the first French painters of the 19th century to turn from Neoclassicism to Romanticism….Decamps also produced a number of genre pictures, chiefly of scenes from French and Algerian domestic life, done with humour. Similarly, in various paintings and sketches he depicted such animals as dogs, horses, and monkeys with a marvelous humour.”^[13]

Le Coup Décisif   

Cabinet des Estampes et des Dessins de Strasbourg, place of conservation of this work.^[12]

Lithographer Jean Georges Frey (1798 – 1852) reproduced this Romantic and genre print named Le coup décisif . While literally translated as a decisive blow, in this case we feel that we are safe translating it as a decisive shot.   

Girls Are Crack Shots With A Marble

We find the little girl in the above print delightful. And we both agree that she is about to take a shot. Of course, if the boy does win the final marble, then they will need to start afresh.

We have always believed that girls can shoot just as well as boys and that their eye-hand coordination is just as good as boys. It is obvious that this game is unsupervised, and it was almost certainly spontaneously organized by the children themselves. We also think it is dimensional. Isn’t that a hole in the ground rather than a flat drawn circle? And finally just look at that little boy’s conical hat! Of course, we welcome any comments you may have about girls playing marbles or any reactions you may have about the print.

Finally, the Triangle

We recently learned about one modern game which uses a flat isosceles triangle with dimensional circles, marbles, placed strategically on the catheti of the triangle as shown below. One marble is placed on the apex. Our triangle is based on the one drawn in the story “Lakhoti” which was posted online by Rishikajadia in 2013.

This story about traditional Indian games notes that Lakhoti is also known as Kancha, Golli, Goti and simply Marbles. Another source tells us that, while India is a phenomenally old and diverse society, Lakhoti is played by children (mostly boys) all over the country. Incidentally, this source also pictures a game of marbles being played with a flat circle.^[15]

Harappan Civilization

In the story Ten desi (traditional) Indian games that will take you back to your childhood we are told that the game of marbles dates to the Harappan Civilization. If this is the case, then Lakhoti is the oldest documented marble play that we have ever found.

“The Indus River Valley Civilization, 3300-1300 BCE, also known as the Harappan Civilization, extended from modern-day northeast Afghanistan to Pakistan and northwest India.

Important innovations of this civilization include standardized weights and measures, seal carving [over 3,500 have been found so far], and metallurgy with copper, bronze, lead, and tin.”^[16]

Playing Lakhoti

This is by far the most complex marble setup we have ever seen. Notice that seven marbles, which are dimensional circles, are placed strategically on a flat isosceles triangle. Note the relative position of each marble.

While it is complex to set up, the game is incredibly easy to play. Rishikajadia, noted above, tells us that a triangle is drawn on the ground with a stick of chalk or with a stick.

We already have a question. How many are allowed to play each game? We ask because if two play then, in theory, each will have to contribute 3.5 marbles! Or one adds three and the second player adds four. If three players add marbles then each has to add 0.77 marbles each!

The author doesn’t explain how best to solve this tiny conundrum. Whenever it has been decided then a shooter fires away at any of the marbles in the triangle from about seven feet away. Again we have a question. Who shoots first? It is apparent that the first shooter has a distinct advantage. How could he miss any of the three marbles on the base line?

At any rate once play is started the shooter keeps each marble that he hits. We can only imagine that a shooter continues to play until he misses. Then another player continues in the same manner until all the marbles are gone.

There is a Contact Us button at the top of this page. If you play Lakhoti or have played it or if you know about it then please contact us and we will tell everyone!

Circles

“Living on a Skyscrapper”^[17]

Playing marbles inside a triangle can be complicated. Drawing and playing inside circles isn’t always a piece of pie! In this game the kids have drawn a chalk circle on the roof of the building where they live. Have you ever seen such a playing ring? It is a circle inside a circle.

Neither circle is absolutely round. Here is a definition of a circle: It is “… a 2-dimensional closed shape that has a curved side whose ends meet to form a round shape. The word ‘Circle’ is derived from the Latin word ‘circulus’ which means a small ring.” ^[18] And that’s why we call them marble rings in the United States.

We have never seen such a marble playing ring! As noted, neither the inside nor the outside ring boundaries are actually round. And they are not concentric rings because they do not share a common center or radius. Technically, the area between two non-concentric circles with different radii is call an annulus.^[19]

Up On the Roof!

We would have expected that the boys would have spread the marbles out in the annulus or the space between the two circles. However, they positioned the six marbles either on the inside circle or just inside the inside circle. And, finally, look how far the shooter is from the rings!

Unlike shooting into a triangle, which has a defined point to shoot from, it looks like each boy defines, a least roughly, how far to shoot from. That is, it seems like the shooter can knuckle down from any position around the circle boundary and he decides how far from the circles that he needs play.

Since the marbles are placed as they are, there would be no advantage to shooting from anywhere around the rings, but, of course the distance the shooter knuckles down may give him a distinct advantage.

Notice the boy in the dark clothing. He has his aggie down on the roof and is ready to shoot next. Doesn’t he look much closer to you than the current shooter?

While we would love to know where these boys learned to make such an interesting ring, we know no more about them and we have never seen another image, old or new, with such a ring.

An Engraving From 1786

Boys Playing at Marbles An engraving from 1786

This is not only old, but very different.^[20] The engraver was Robert Pollard (1755 – 1838). “He moved to London in 1774 and trained under painter R. Wilson and engraver I. Taylor. By 1781 he had settled in Islington, where he set up as an engraver and publisher. Many of his prints combine different methods of engraving, although aquatint was often added by a specialist.”^[21] If you want to know more about aquatint then you might want to check “What is an aquatint?” at https://www.finerareprints.com/blog/what-is-an-aquatint .

The Yale Center for British Art tells us that the aquatint for this engraving is by Francis Jukes (1747 – 1812) and that it was published by James Birchall.^[22]

What Are They Doing?

The Musées de Strasbourg description of the action: “In an interior, four boys of different ages are playing marbles. In the foreground, a small bag with the marbles escaping from it is half hidden by a white fabric. On the left is the hat of one of the boys where four marbles are placed. In the background, two little girls, the oldest of whom holds the hands of the youngest. Behind, a schoolboy stares at the scene.”

We don’t see four boys. It appears that there is a gentleman to the right in the print. He appears to be encouraging the shooter, and, if so, then this may be a supervised marble game.

We were wondering what the hat is and now we wonder what that “white fabric” is that covers the marble bag. And it looks to us like there are six marbles lined up like the seven we discuss above and which are inside a triangle.

In this print the boys are shooting at a cross^[23], made up of marbles, from some distance away and on a tile floor. If the shooter hits a marble, then how do the players know that it is “out of the ring”, since there is no circle boundary, and that it now belongs to the shooter? As usual we have more questions than answers, but we are glad to see that over the centuries and across the continents there are and historically have been so many ways to play marbles.

Who Needs a Ring, a Triangle, or a Hole in the Ground to Shoot Marbles?^[24]

This photograph dates to 1901 and the photographer was John H. Tarbell (1849 – 1929). Tarbell had a studio in Asheville, North Carolina, from 1896 – 1901. Tarbell’s images depicting African Americans in the southern parts of the United States were widely published during the early part of the twentieth century and appeared in publications including Cosmopolitan and New England Magazine.

We cannot be certain if these children are coming from work or going to work, but this photograph illustrates our point  in the section “Let’s Regroup and Review” above. There was a time in America when children worked hard but still found time for playing marbles.

Straight Line

Long Short Story

Yes, this is a long short story; it’s time to take our marbles and go home. But we have learned a lot about when and how children learn to distinguish depth, shapes, and space relationships. With practice comes eye and hand coordination. Without supervision children make the rules of play, the arrangement of the marbles inside a triangle, a circle, more than one circle, or a hole or series of holes in the ground. Children decide who and who cannot play. They agree about whether to keep their winnings or just to play for fun. And over the years they become adept at settling arguments.

Marbles and a triangular field of play are still popular today. Some children play every day. And there are about 480 million children in India under the age of 18. Marble play in India goes back centuries.

We close with many questions, but one really nags at us. We know that children with no or very little formal education did and do play marble games with others successfully and unsupervised. Exactly where do they get the skills of space, shape, place, and dimension that they have to have to play successfully? If you know or simply have some keen speculations then please do press the Contact button and let us hear from you!

1. “Marble Time” Stereograph c. 1891. LC-Dig-stereo-1s44055 (digital file from original) LC-USZ62-61810 (b&w film copy neg. of left half of stereo. Fellows Photographic Co., publisher. ↑
2. Matthew Wills supports this notion that “Marbles were a form of spontaneous and unsupervised play, organized and policed by the players themselves.” In “Losing Our Marbles” June 25, 2018. @ Daily Jstor https://daily.jstor.org/losing-our-marbles/ 9/18/2023 ↑
3. While we have been unable to gain publication rights to this photograph, you can see it, along with its write-up @ https://histclo.com/act/out/game/marb/aom-france.html. ↑
4. Bing Chat with GPT-4 (9/23/2023) https://www.momnewsdaily.com/preschools/when-do-kids-learn-shapes/ ↑
5. This source is “25 Creative Activities and Ideas For Learning Shapes”—We Are Teachers @ https://www.weareteachers.com/learning-shapes/ (9/24/2023) ↑
6. This photograph is untitled, but the Library of Congress notes that it relates to playing marbles on the first warm day of spring. It was taken in 1940 by Lee Russell. LC-USF33-02580-M1 (b&w film nitrate neg.) LC-DIGfsa-8a27920. U.S. Farm Security Administration/Office of War Information Black & White Photographs. ↑
7. “What Children Know and Need to Learn about Shape and Space.” by Herbert P. Ginsburg and Colleen Oppenzato @ https://prek-math-te.stanford.edu/spatial-relations/what-children-know-and-need-learn-about-shape-and-space 9/25/2023↑
8. You might want to check “Circles: Diameter, Chord, Radius, Arc, Tangent” @ https://www.onlinemathlearning.com/diameter-of-circle.html 9/25/2023.
9. https://www.sparknotes.com/math/geometry2/specialtriangles/section1/ ↑
10. Discovering Shapes and Space in Preschool | NAEYC 9/23/2023 ↑
11. What age should child know shapes and colors? – Think Tank Scholar 9/23/2023 ↑
12. Le coup décisif 77.2012.0.115 Decamps, Alexandre Gabriel, Dessinateur; Frey, Jean Georges, Lithographe. Special thank you to Catherine Paulus, Assistante de Conservation, Documentation / Photothèque des Musées de Strasbourg ↑
13. https://www.britannica.com/biography/Alexandre-Decamps 9/29/2023 ↑
14. Understanding Children’s Drawings & Stages of Development – how we montessori (9/23/2023) To learn more about Piaget you might want to check “Jean Piaget Swiss psychologist” @ https://www.britannica.com/biography/Jean-Piaget 9/28/2023↑
15. https://blogs.languagecurry.com/articles/traditional-desi-indian-games-and-sports-for-children-and-adults 9/29/2023 ↑
16. https://www.khanacademy.org/humanities/world-history/world-history-beginnings/ancient-india/a/the-indus-river-valley-civilizations 10/2/2023 ↑
17. Photograph. LC-DIG-ggbain-01391 (Digital file from original glass negative. Bain News Service, publisher. Library of Congress, Prints & Photographs Division. LC-B2-1234. ↑
18. https://www.cuemath.com/geometry/circles/ 10/2/2023 ↑
19. https://mathworld.wolfram.com/ConcentricCircles.html 10/2/2023 ↑
20. Cabinet of prints and drawings. Boys Playing at Marbles 77.2023.0.177 Pollard, Robert, Engraver 1785 Pay, Richard Morton, according to – Securities): Boys Playing at Marbles Author(s): Robert Pollard (1755 – 1838), Engraver Richard Morton Paye (1760 – 1821), after Francis Jukes (1745 – 1812), Engraver Creation date(s): 1785 Materials): Paper Techniques): [Technique Mixte] Aquatint Dimensions): Height in cm: 40.2 Width in cm: 52 Identifier: 77.2023.0.177 Areas). Special thank you to Catherine Paulus, Assistante de Conservation, Documentation / Photothèque des Musées de Strasbourg ↑
21. https://artcollection.culture.gov.uk/person/pollard-robert/ 10/2/2023 ↑
22. https://collections.britishart.yale.edu/catalog/tms:22282 10/2/2023 ↑
23. While researching this story we found one photograph, with a short write-up, of boys apparently playing marbles with 13 marbles in a cross design. It was a staged photograph with some type marble trophy between them. McDaniel, Travis H. “Vanishing Georgia—An Old-Fashioned Boyhood” Georgia Backroads (Winter 2010), pages 14 – 20. ↑
24. “2 African American shoe shine boys playing marbles.” c. 1901. Library of Congress Prints and Photographs Division, Washington, D.C. Call Number/Physical location LOT 11826 [item] [P&P] LOC number 2016652686 ↑