Engman was born in 1927 to parents who had emigrated from Sweden. He joined the Navy at the age of 15, serving in World War II in the Pacific. He graduated from the Rhode Island School of Design with a BFA, and from Yale University with an MFA in 1955, in Painting and in Sculpture, where he studied with Josef Albers.
Penn students collaborated with him to create the Peace Symbol sculpture in front of the Van Pelt Library.
One of his best-known sculptures, entitled "Triune", created in 1975, stands in Philadelphia at the south west corner of City Hall. Another, "Kings" is at 78th and Lindbergh Streets, also in Philadelphia. In his work, he often explores minimal surface intersections of geometric forms, which has led to the interest over the years, of many who are involved in the science and mathematics of such surfaces, including the late R. Buckminster Fuller.
After B. K. S. Iyengar in at Morris Arboretum, 9414 Meadowbrook Avenue, English Park Step Garden, Philadelphia.