Just when I thought I might have a somewhat organized, productive morning, the electricity went out. One of the coldest days of the year, so the house cooled down fast. I put my coat on and sat by a window to read, thinking how grateful I was NOT to be a lineman working to get the power back on. Sure am looking forward to warm weather again, someday...
This month's playful math snack is "string" art. While our designs are made with markers or colored pencils, this sort of math art originated as "curve stitching" with silk thread in Mary Everest Boole's 1904 book The preparation of the child for science.
I've created a printable worksheet, but your children can also make their own designs — creating an original math art project is usually more rewarding than following another person's pattern.
Have fun playing math with your kids!
P.S.: I'm running another math book giveaway, on my blog this time. If you'd like to enter, the information is here.
Finally, I'm not sure if I've mentioned it, but my Prealgebra & Geometry Games book is now available for preorder at all the regular bookstores (ebook and paperback). Publication date is February 23!
Valentine Math Art
Follow this link to download the Heartstrings pattern. Use colored pencils or markers to connect the dots.
Each quarter of the page is a string-art design consisting of two lines that meet at that corner. The two hollow dots on the right and left sides of the page are used twice (for the top and bottom patterns), as are the dots at top and bottom center.
For each corner pair of lines, connect the farthest-out dot on one of the lines to the closest-in dot of the other. Then continue from one dot to the next, letting the lines criss-cross to create the design shown.
A cardioid is a heart-shaped curve traced by one fixed point on a circle that rolls around the circumference of another circle with the same radius.
This free "Draw a Cardioid" project is string art for middle or high school students. It takes some careful ruler work, lining up the points, but my students were delighted to see the heart appear as if by magic.
After trying their examples, make up a design of your own. Use a ruler or any straight edge to draw two lines. The lines can meet at a corner, or they can cross, or they can each stand on their own. They don't even have to be straight (the cardioid used a circle). Every combination will make a different design, so experiment to discover what you like best.
Mark dots along your lines. Start with evenly-spaced dots, or experiment with other spacings. Now choose a pattern for connecting the dots. Traditional string art connects crosswise — matching the farthest dot on one line to its opposite, closest-in partner on the other — but different connecting rules create their own cool designs.
The Art of Calculus
Don't you love how the straight lines of string art form an illusion of graceful curves? In calculus, we also use straight lines (the derivative) to help us "see" curves more clearly.
Try drawing a simple curve and finding several tangent lines, the derivatives of the curve at those points. How might you create that curve using string art?
“Stitching a curve from its tangents is no more straining to the brain and nerves than stitching round a printed outline.
“The difference is that the act of evoking a curve 'out of the everywhere into here' by simple obedience to a rhythmic law lodges an impression on the unconscious mind.
“This impression will be ready to surge up in ten years' time, and perhaps make some teacher wonder why this boy or girl never had the least difficulty in grasping the idea of the differential calculus.”