Pythagoras and Eithne

I remember well the day I fell in love with geometry.  I was 10 or 11 years old and had recently been exposed to it in school.  At first it was merely another subject, like geography or English Literature, and it didn’t seem any more useful than either of those.  It was just another way of disciplining kids in educational institutes while their parents worked.  Grandparents wondered how on Earth it would help us make a living in the real world of roads and buses, farming and food production.  I had no answer until that day in the backyard with my little five-year-old sister, Eithne.  We were playing under the apple tree when she asked, “Seán, how tall is the apple tree?”  I said, “Let’s measure it!”  Now our mother, Peig, was a seamstress, so there were lots of six-feet-long cloth tape measures in the drawers of her Singer Sewing Machine.  Eithne ran and fetched one and we began climbing the tree; but the top branches were very thin and weak.  We could neither stand on them nor persuade the end of the tape measure to stay put as we attempted to throw it atop the highest twig.  It was frustrating and not a little dangerous.

And that was when I got the brainwave!  I said, “Let’s climb down, I’ve got a better idea.”  I ran into the house and returned with my camán (hurley), a curved ash instrument used in an ancient Irish game called, Iománaíocht, that dates back to 1287 BC.  I measured the camán; it was 36 inches tall.  I stood it upright beside the apple tree and asked Eithne to hold it firmly in a vertical position.  Then I measured its shadow; this was 48 inches long.  I told Eithne, “the relationship between my hurley and its shadow is 36 to 48; that’s the same as 3 to 4; so, it’s going to be the exact same relationship between the apple tree and its shadow.  So now all we’ve got to do is measure the length of the tree’s shadow!”  We did.  It was 24 feet long.  “Now,” I pronounced with Pythagorean certainty, “that means that the tree is 18 feet tall.”  She was almost as thrilled as I.  We looked around the backyard; over near the fence was tip of the shadow of the chimneystack on the top of our two-storey house.  My heart leaped for joy.  “Here” I said to Eithne “hold the tape at the foot of the wall of our house.”  And we marked off our measurements with our little six-feet-long cloth tape measure.  The shadow of the house, complete with chimneystack, was 32 feet long; which meant that the house plus stack was 24 feet high.

By now I was in a mystical state.  I said to Eithne, “I know what we’ll do, let’s go up to Spillane’s field (the local farmer) and measure the tallest tree there!  We ran through the house, out the front gate, across St. Joseph’s Park and up the Bóthar Buí (the Yellow Road) ‘till we reached the first of Spillane’s fields.  We climbed over the fence and there, in a corner, standing alone in all its glory was a magnificent sycamore tree.  Eithne held the tape to the gnarled base, and we measured off its shadow.  It was 96 feet long, which told us that the great tree was 72 feet high.

Almost as high as I myself was in that moment.