Designed by Bernard Montgomery in 1940, when he commanded the division, the design represented a combination of threes: the 3rd Division, which contained three brigades with each brigade consisting of three battalions. The red triangle has been described as the core of the division, the command element. Per the Imperial War Museaum, less serious interpretations have been offered such the division's three brigades (the black triangles) are bound together by blood (the red triangle); another suggested the brigades being tied together by red tape.
This photograph INS 6623 comes from the collections of the Imperial War Museums.
Original: Bernard Montgomery Vector:  Fallschirmjäger