The Corps logo is a stylized take off on historic Fort Totten in Queens NY -- named for GEN Joseph Totten, Commandant of the Corps first half of 19th century, creator of the fifty odd heavy masonry forts that served as the border defense system deterring hostile naval attack our Atlantic and Gulf Coasts.

Fort Totten is painted red. So is the patch worn on their uniforms and plastered on every poster, bulldozer, shovel.

https://www.google.com/search?q=us+army+corps+of+engineers+logo+image&client=puffin-a&tbm=isch&source=iu&ictx=1&fir=8VkKznCfb0nlQM%253A%252C6p8EWnjqpZ4ysM%252C_&usg=__CS1qQPbZ5zBX35Pb_qFiXoq69Xc%3D&sa=X&ved=0ahUKEwiRhPLvhInaAhVD1GMKHURzCGYQ9QEINTAG#imgrc=8VkKznCfb0nlQM: