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A floor by the stairs is tiled with six-sided shapes. No gaps. No overlaps.

What this track covers

• Copy a corner. No protractor (angle measurer) needed.
• The perpendicular bisector. Every point is the same distance from two ends.
• Split a corner. Two halves that match.
• A parallel through a point. A line with the same gap everywhere.
• A triangle from three lengths. Base, arc, arc, join.
• A triangle from two lengths and the angle between. A second method.
• What a tiling is. No gaps, no overlaps.
• Why some shapes fit. Tile corners at one point add to 360°.
• A square line. A perpendicular, at 90°, through any point.
• 60°, 30° and 15°. One equilateral triangle, then bisect (halve) the corner.
• A hexagon. Mark the radius again and again round a circle.
• The tangram. Seven pieces, each a share of one square.
• Tiling the whole floor. Which regular shapes fill a point.

Most of this is Chapter 6 of Part II, Constructions and Tilings. The two triangle methods are also in Part I, Chapter 7. Bring a compass.