Week 08 · Circles
Shop Day
Shop Day: the family circle
// The turntable and the spotlight
⏱ about 20 min
Shop Day: The Family Circle
Comet winds the chalk string around her hand at the shop door. "Shop Day. A circle at home, as big as you can."
"Then the three tests," Wren says. "Walk the rim with string and compare it to 3.14 times the diameter."
"Find the center with a book corner," Comet adds. "And measure one inscribed angle against its arc."
Nova dims to a soft glow. "Would you like a hint? Mark the center before anyone steps on the chalk."
"Our designer, your family is the shop crew," Comet says. "One holds the pin, one walks the chalk, one measures."
"And the sidewalk washes clean," Wren says. "Chalk only. Nothing permanent."
- All circles are similar: a dilation from the center carries one onto another.
- A central angle equals its arc. An inscribed angle is half its arc. An angle in a semicircle is 90°.
- A tangent is perpendicular to the radius. A radius perpendicular to a chord bisects it.
- Opposite angles of an inscribed quadrilateral add to 180°.
- Arc = (angle ÷ 360) × 2πr. Sector = (angle ÷ 360) × πr². Arc ÷ radius is the angle in radians; 180° = π.
◇ CHALK CIRCLE, THREE TESTS
Outside on a sidewalk or driveway, or on a big sheet of cardboard, draw a circle with chalk tied to a string.
Test 1: lay string around the rim, then measure the string. Measure the diameter. Divide. Is it close to 3.14?
Test 2: set a book's corner on the rim and mark where its edges cross the circle. Join the marks. Does the line pass through the center?
Test 3: mark two rim points, measure the central angle, then measure the angle from a far rim point. Is it half?
Test 1: lay string around the rim, then measure the string. Measure the diameter. Divide. Is it close to 3.14?
Test 2: set a book's corner on the rim and mark where its edges cross the circle. Join the marks. Does the line pass through the center?
Test 3: mark two rim points, measure the central angle, then measure the angle from a far rim point. Is it half?
For a grown-up
Choose a flat spot away from the street. Chalk only, and it rinses off.
Hold the pin or the string's center end so the circle stays round.
A protractor and a tape measure are all the tools needed. Use 3.14 for π.
Hold the pin or the string's center end so the circle stays round.
A protractor and a tape measure are all the tools needed. Use 3.14 for π.
CIRCLE CHECK
- Read the question.
- Tap your answer.
Your chalk circle has radius 1.5 meters. About how long is its rim, in meters? Use 3.14 for π.
You mark two rim points 100° apart as seen from the center. What should the angle from a far rim point be?
On the 3 meter turntable, how long is half the rim, in meters? Use 3.14 for π.Draw your chalk circle with the diameter you found, the book corner on the rim, and the angle you measured.
Three tests, one circle, no tape measure across the middle. Next week the stage grid gets taped and every mark gets coordinates.