The text below was copied from the 36th Armored Infantry Regiment, 3rd Armored Division Historical and Pictorial Review ("yearbook") dated 1942. It is listed as Published and Copyrighted 1941 by The Army and Navy Publishing Company, Inc.
Of special interest is the last paragraph which states that the divisional patch is to be worn on the left breast of the field jacket! It is doubtful that this practice continued after the division left the U.S.
The colorful triangular shoulder patch worn on the left shoulder ofsoldiers and officers of the 3rd Armored Division has a history, one that is varied and dates back to the old tank battalions of World War days. To it have been added additional symbols.
Forming the basic pattern of the insignia are three equal segments of yellow, red and blue. The yellow, on top, represents the cavalry, the blue in the lower left hand part of the triangle represents the infantry, and the red in the lower right the artillery.
Superimposed on the three equal sized torques is the insignia of the Seventh Cavalry Brigade (Mechanized), one of the first mechanized units of the new Army. The combination of the insignia of the old tank battalions and the cavalry brigade is symbolic merging of those arms as the progenitors, or parent organizations of the Armored Force.
The Seventh Cavalry Brigade's insignia is a tank track, representing mobility and armored protection, a cannon running diagonally across the tank track, representing fire power, and a red bolt of lightning, representing shock action.
The cannon and tank track, outlined n black, represent a general's command - in this case the command of Major General Walton H. Walker.
The "3" at the top represents the Third Armored Division.
The patch, in addition to being worn on the left shoulder of the blouse, or coat, is worn on the left breast of the field jacket."