* Heawood's conjecture: This conjecture, later proven by Ringel and Youngs, states that any map on a surface with genus *g* can be colored with at most *χ(g) = max{⌊(7 + √(1 + 48g))/2⌋, ⌈(7 + √(1 + 48g))/2⌉}* colors, where ⌊x⌋ is the greatest integer less than or equal to *x*, and ⌈x⌉ is the least integer greater than or equal to *x*.
* Heawood's formula: This formula gives the chromatic number for a torus, which is the surface of a donut. It states that the torus can be colored with at most 7 colors.
* The Heawood Graph: A specific graph which is used as a counterexample to a conjecture about the number of edges in a graph with a given number of vertices.
While his work is focused on map coloring, he also published works on:
* Algebraic geometry: He contributed to the study of algebraic curves and surfaces.
* Number theory: He studied number theoretic properties of surfaces.
* History of mathematics: He wrote articles on the history of mathematics, particularly on the work of mathematicians from the 19th century.
However, Heawood did not write any books. His work primarily consists of research papers and articles published in academic journals.