Math circle 2.10 and 2.11

Making Henna, Talking about Petes

The story of last week’s Math Circles is best told in photos, over 50 of which you can see here.

But here are a few details.

In order to make up a snow day we had 2 sessions.  On the first (Monday, February 10), Gina helped me and the students mix up our own henna pastes.  The recipes gave henna powder measurements by both weight and volume, so we debated which tool would be more mathematical to use: a scale or measuring cups. (And which would be more scientific?  And what are some shared goals of both math and science?)  Then we tested two different recipes.

We also rolled cones to use as henna applicators. We experimented starting with different shapes, seeing that a 3D shape can be created from various 2D shapes when overlap is allowed.

Monday’s session was an awkwardly small group of 3, but it was okay because these particular kids have known each other for years.  Still, way more conversation would have happened had our whole group been there.  There were quiet times when Gina and I conversed about math and art, with the kids listening and occasionally offering questions and comments.

Then Gina took the new henna paste home to cure under a heat lamp overnight.

On Tuesday (February 11), our bigger group put the new pastes into tubes.  Gina and I had debated on whether to include the henna-paste-making process in this course, since you can simply buy it ready to use.  And henna-making isn’t exactly math or art.  But science intersects with both of these disciplines.  (I might even put forth that no disciplines exist in isolation.) In the course, we have a bent toward history, authenticity, and full process, so we want the kids to know what work goes into making this material.  Besides, making it from scratch costs about 1/10 the price of store-bought.

We had at least one mathematical aha moment.  “A true line is impossible to draw from material tools,” I read to the kids from Schneider.

“What do you think he means by that?” I asked the kids.  We debated, tried to define a line, and got more confused.  Then I drew a line segment on the board and measured it.  Whoa – it was 150mm by 3mm – it had a width!  It was a rectangle, not a line segment, after all.

“A drawn line isn’t a real line; it’s a symbol of a line,” X summarized nicely for us.  Likewise, we realized, you can’t draw a circle, only a symbol of a circle.  What is the name of the shape you really draw when you attempt to draw a circle?  A bagel?  A donut?  The kids didn’t know. Do you?  I told the kids that I also couldn’t remember the mathematical name for that shape, so desperately tried to find it online before class.  I unexpectedly found it on a Swahili website.  It’s called a “pete” in Swahili, known more commonly in English as a ring.  (So obvious with our 20/20 hindsight.)

As Gina worked with the kids on using transfer paper to copy designs onto skin, I read a bit more from Schneider, and began a massive list of various interpretations of geometric symbols/shapes.  We discussed the inherent tension in the dyad/line/number 2.  “Like mother-daughter tension,” added a student.

Before I pass the baton to Gina Gruenberg, here’s the link to last week’s photos (  Thanks to several of you for reminding me to put those photos in.


 This week I had the good fortune of being part of the Math Circle on Monday (a make-up class) and Tuesday.  What a great group of kids and a fun way of learning math.  I wish I had learned math this way when I was growing up!  On Monday, perhaps due to the cold and the day, we only had three students, but had fun making henna paste using two recipes.  The recipes are below.  We used a scale to measure the first batch of henna powder in grams. This powder, called Jamila, is from Pakistan; it comes packaged in a 100 gram foil sealed package from Henna Caravan in California. Each recipe contains:

•   a liquid that is acid: lemon or tea,

•   a mordant: the dye fixative which releases the dye from the mixture so that the Henna paste creates a temporary stain on the skin. Specific essential oils, also known as “terps” are recommended as mordants for Henna; the gentlest one is Lavender Essential Oil which is especially good for children and pregnant women.  Henna Caravan sells organic or wild crafted, pesticide free essential oils.  The other oil that I ordered for the class is their signature essential oil blend: Melaleuca Cajeputi, Wild Orange and Lemongrass oils from Australia.

• sugar: this ingredient, used in the lemon recipe, helps the henna adhere to the skin

Following Rodi’s discussion last week about circles, we looked at the Olympic Logo of 5 interlocking circles and began discussing their significance as well as the Continents in the world, where Henna grows (ie. which continents) and the number of continents represented in the Olympics (5). 2  Since 5 was the number of the day, I showed them the significance of the number 5 in Moroccan Henna.  Moroccan Henna designs are most often used for protection and fertility.  Henna is believed to contain “Baraka” or good luck; the henna designs are seen as talismans or blessings on the skin.  The number 5 is linked to the hand, the 5 fingers and protection symbols.

I took the Henna paste that we mixed home to keep warm under a lamp so that the dye would release for Tuesday’s class.  Then I brought it back and showed the kids how to make (cut, roll and tape) and fill cones.  The cones – or applicators – are one way of applying the paste to the skin.  We may also try paint brushes and other tools of their invention.  We also explored using spirit transfer paper so that we could transfer designs that they made on paper to the skin. This is what tattoo artists use for transferring designs and I asked who knew the difference between a Tattoo and Henna. 

•“Tattoos are permanent,  Henna is temporary.”

•“Tattoos can be colored, Henna is orange, or shades of brown and burgundy.”

“T” told us that in gymnastics meets Henna is not allowed, so I made some tubes of colored gel (also from Henna Caravan and made with gel and Mica for body art). It can be applied like Henna, washes off and can even last for a day or two if  not washed.

• “Tattoos are made using needles, henna is a paste.”

•  Tattoos are typically single images while Henna is a series of patterns which in India and Morocco traditionally cover the arms, hands, legs and feet like a lace glove.

Henna has been around for over 5000 years and dates back to the Egyptians. The prophet Mohammed used Henna to color his beard, Henna was found on mummies as well.  Tattoos are comparatively a much more recent art.  (17th or 18th c) 

*As far as I know, tattooing is not a group activity as is Henna, which traditionally has been used for celebrations and rites of passage.  (weddings, births, etc)

 1 Michael Schneider, A Beginner’s Guide to Constructing the Universe, p23

2 The Olympic rings as a symbol of continents is debatable from a historical perspective, but we do know the provenance of the colors of the rings.

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