Much of the design influence though has little or nothing to do with Islam itself, but the Arabic culture and design, some of which predates Islam by hundreds if not thousands of years. Part of this influence stems of the invasion of destruction of the Byzantium Empire. The Christian capitol fell to Islam. The fact that Europe suffered several such invasions, it is not hard to imagine that much of old Europe would be influenced by the encroaching culture. These events though predate US history by nearly a thousand years, though. In short, specific words, architectural design, math, and such were in western culture before the US was formed. To say that Muslims directly impacted early US culture is a stretch of the imagination.