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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

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A Sameness Surely

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

Logo Challenge 3 - Star Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1
Each of the following illustrate a nested REPEAT.
The first example is for a circle based on squares, the second for hexagons.

Note that for the square the inner REPEAT means you move along six sides. This seems redundant but it is a way to get the turtle to a position which means it is ready to draw the next square.

A similar strategy has been applied to the hexagon pattern with REPEAT 9 not REPEAT 6.

to SQSP

REPEAT 12 [REPEAT 6 [FD 30 RT 90] LT 150]

end

and
to HESP

REPEAT 8 [REPEAT 9 [FD 30 RT 60] LT 135]

end