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Dec 03

Milli-Lincoln

Both classes zoomed in on pennies, wood grain, whiteboard eraser, and more.  Many US cents have President Lincoln on the front and his Washington DC Memorial on the back.  Microscopes reveal a faint outline of Lincoln sitting in the Memorial and a duck or goose climbing the stairs.  We used this activity to launch a mathematical problem: How many atoms thick would Lincoln’s hair be if the tiny image of him in the Memorial had hair?

We measured the Memorial columns, finding 1 millimeter horizontal centers, and approximating Lincoln’s shoulders spanning half that width.  We measured our own shoulder width, rounding up to 50 centimeters to keep the numbers easy.  The ratio of 0.5 millimeter to 50 centimeters (5*10e-5 : 5*10e-1) is 1:1000, making the image a “Milli-Lincoln”.  We computed using powers of ten because learning the power of exponents was my motivation for this exercise.

Students asked for information necessary to calculate the thickness of Lincoln’s hair in atoms: thickness of human hair, thickness of atoms.  We approximated human hair, which varies from 17 – 181 microns, as 100 microns or 1*10e-4.  We approximated the width of an atom as 1 angstrom or 1*10e-10, though atoms more massive than hydrogen have larger diameters and this also depends on their neighboring atoms.  By these numbers, human hair is 10e-4 / 10e-10 = 10e6 = a million atoms thick.  Milli-Lincoln’s hair would be 1/1000 as thick, or 1000 atoms.

We practiced multiplying and dividing exponents of ten. The afternoon class graphed the exponent against the value of the expression, watching the curve snuggle against the X-axis without reaching it.

The afternoon class also reviewed individual projects, with Max presenting on his energy-capture project that could be incorporated into a soccer ball.  Carlin outlined his tire pressure vs. traction measuring machine.  Jeanette explored lava lamps we could make with wax, crayons, or other materials.

The morning class researched specifications of infrared/non-contact thermometers, with Myles and Nathanael finding that the highest temperature that the best thermometer we have in class (900 C) is lower than the higher temperatures reached in a candle flame (1400 C).  Myles’ Grainger catalog offers a model that measures to 1550 C, but costs $335. The great 19th Century scientist Michael Faraday said that all science could be explained through a candle.  Even if only the science known then could be so explained, that’s still impressive.

Jeanette focuses microscope Lincoln in his Memorialfowl on steps of Memorialwood grain white board eraserwhite board Lincoln PM white board Lincoln AM 2 white board Lincoln AMCarlin and Max graph exponential curvecandle flame temperature

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