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Geometry 9-12 / Week 01 / Thursday
4/6
Week 01 · Points, Lines and the Chalk Grid

Thursday

The turntable data
// Precise words and string-and-chalk constructions
⏱ about 20 min

Thursday: The Turntable Data

Wren unrolls the tape across the turntable platform. "Radius 1.2 meters, center to edge. Comet, hold the string."

Comet pins the string at the center mark. Wren steps the chalk around the rim. Six marks appear.

"Now the chords," Wren says. "Neighbor to neighbor, then every other mark. What do you notice?"

"Neighbor to neighbor is 1.2 meters, same as the radius," Comet says. "Every other mark is longer."

Nova projects a hexagon over the six marks, then a triangle over three of them. "Would you like a hint? Count the gaps."

"Six gaps around the center. One full turn shared six ways," Wren says.

"Spokes for the hexagon, spokes for the triangle," Comet says. "Our designer, read our table and check every number."

The crew's turntable table

Every number here is the crew's own made-up Scene Shop measurement in meters and degrees. Nothing is a real-world fact.

MeasurementValue
radius (center to rim)1.2 m
chalk marks around the rim6
chord, neighbor to neighbor (hexagon side)1.2 m
chord, every other mark (triangle side)2.08 m
hexagon perimeter7.2 m
angle between neighboring spokes60°
angle between triangle spokes120°
each corner angle of the hexagon120°
A circle of radius 1.2 m with two spokes 60 degrees apart and the chord joining their rim marks.

The spokes to two neighboring marks make a 60° angle. The two spokes and the chord make a triangle with two equal sides.

Its other two angles share the rest of 180° equally, so all three are 60°. That is why the chord equals the radius.

For the triangle, the marks are two steps apart. The chord is 2.08 meters, measured on the platform.

A triangle with three 60 degree angles and three equal sides of 1.2 m, the spokes and one chord.
READ THE TURNTABLE TABLE
  • Read the question.
  • Tap your answer.
Six chalk marks are spaced equally around the turntable rim. What angle, in degrees, is between neighboring spokes?
The triangle uses three of the six marks. What angle, in degrees, is between neighboring triangle spokes?
The six chords make a regular hexagon on the turntable. What is each corner angle of the hexagon, in degrees?
LENGTHS ON THE TURNTABLE
  • Read the question.
  • Tap your answer.
The radius is 1.2 meters. How long is each side of the inscribed hexagon, in meters?
Each hexagon side is 1.2 meters. What is the hexagon's perimeter, in meters?
The triangle side joins marks two steps apart. Which length did the crew measure for it, in meters?
The angle between neighboring hexagon spokes, in degrees. Type the number.
WHY THIS EXERCISEThe spoke angle is what makes every chord equal, so the hexagon is regular.
StatementTrue or false?
Each hexagon side on the turntable equals the radius.?
The triangle side is shorter than the hexagon side.?
The six spoke angles add to 360°.?
The square in the circle would use four marks spaced 90° apart.?
WHY THIS EXERCISEReading the table against the construction shows why the hexagon, triangle and square all fit a circle.
A square inscribed in the turntable circle uses four marks. What is the angle between neighboring square spokes, in degrees?
The triangle on the turntable has three equal corner angles. How many degrees is each one?
Try it
On paper, draw a circle with a radius of 6 centimeters. Step the compass six times around it and join every other mark.
Measure the triangle side. Divide it by the radius. Compare with the crew's turntable ratio.
Draw the turntable circle, its six marks, the hexagon, the triangle and one spoke angle of 60° labeled.

Sharp reading, designer. Tomorrow you find constructions in everyday life and review the week.

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