Read the hypocycloid writeup first. The deltoid is a plane algebraic curve. It is the hypocycloid such that the radius of the fixed circle is 3 times the radius of the rolling circle, a say. It looks like a triangle where the edges of the triangle have been curved toward the centre.

An equation for the deltoid is

(x² + y²)² - 8ax(x² - 3y²) + 18a²(x² + y²) = 27a⁴.

Look at your shoulder, this is the muscle that is there. It allows rotation and other shoulder based movements of your arm.

Del"toid (?), a. [Gr. deltoeidh`s delta-shaped; de`lta the name of the letter ei^dos form: cf. F. deltoide. See Delta.]

Shaped like the Greek (delta); delta-shaped; triangular.

Deltoid leaf Bot., a leaf in the form of a triangle with the stem inserted at the middle of the base. -- Deltoid muscle Anat., a triangular muscle in the shoulder which serves to move the arm directly upward.

 

© Webster 1913.