To Draw a Deltoid (First Method)

Draw a circle, centre O, and a diameter D'OD. Mark points on this circle at intervals of 5°, starting from D, and number them 0, 1, 2, 3, …, in anticlockwise order, the point D itself being numbered 0. Number alternate points again, starting from D', in clockwise order, the intervals 0 to 1, 1 to 2, etc., being now 10° instead of 5°. Join the pairs of points having the same numbers, continuing until a threecusped curve is completed. This curve is the deltoid. (Fig. 51)

Suitable Dimensions

It is again convenient to use a semi–circular protractor. If its radius is 2 in. the centre should be 3¼ in. from the Left–hand edge of the paper. With paper 3P the whole curve can then be drawn, but with narrower paper one cusp will be cut off.

Envelope of Diameter of a Rolling Circle

In Fig. 52, a circle of radius a, on D'OD as diameter, is drawn as before, and Q', Q are a pair of corresponding points, with angles DOQ, D'OQ' equal to t and 2t respectively. A circle is drawn with centre O and radius 3a, meeting D'OD produced at A' and A. A variable circle is now drawn with centre Q and radius 2a, touching the outer fixed circle at I and the inner fixed circle at J. Q'Q is produced to form a diameter P”P' of this circle.