|Large circle in Jordan|
|Large circle in Ohio|
Diffusionists have pointed to many links between the Old World (Africa, Asia, Europe) and the New World (The Americas), ranging from plants (includint cocaine) to various architectural styles. The most common is probably the pyramid, famous in Egypt and Mesoamerica (as well as Sudan, Peru, and other areas), but there are also artistic links, such as figures with two left hands, which appear in relief sculptures and paintings in Egypt and Mesoamerica. Here's an examination of this connection, for example:
John Sorenson's book lists many more, including plants and architecture. Mesoamerican theorists use these links as evidence of a connection between the Middle-East and Mesoamerica. See, e.g., Wirth's book. There are links in terms of measurements as well, as Garth Norman points out here.
One link that I've so far never seen addressed by the Mesoamerican theorists is the unusual creation of large circles in the Middle East (mainly Jordan) and in North America (mainly Ohio area). The Jordanian circle in the photo above is 1,280 feet in diameter. The Ohio circle in the photo above is about 1,050 feet in diameter. There are at least five such circles in Ohio that are around 1,500 feet in diameter, along with several other sophisticated earthworks.
What all this tells me is that there may have been ancient cultural exchanges between Mesoamerica and Egypt/Babylon/Assyria, (but of course there are many critics of diffusionism generally and in Mesoamerica specifically). In terms of the Book of Mormon, none of these links are required or prohibited by the text. They are simply and completely irrelevant, other than to establish the plausibility of a transatlantic voyage by ancient people.
What the text does require, however, is a connection between Israel/Jordan and the Book of Mormon lands, in terms of language, observing the Law of Moses, building temples, and other cultural elements. In Ohio, we know that some of these earthworks were used as observatories. Others we don't know the purpose of. We don't know the purpose of the circles in Jordan, either, but it will be interesting to follow the research.
According to the Smithsonian Magazine: