Paper × 841 mm). A1 is half the size of a sheet of A0 (i.e., 594 mm × 841 mm), such that two sheets of A1 placed side by side are equal to one sheet of A0. A2 is half the size of a sheet of A1, and so forth. Common sizes used in the office and the home are A4 and A3 (A3 is the size of two A4 sheets). The density of paper ranges from for tissue paper to for some speciality paper. Printing paper is about . Paper may be classified into seven categories: Some paper types include:
Mathematics of paper folding produced using a non-folded crease in the paper, as is easily done with wet paper or a fingernail. Assigning a crease pattern mountain and valley folds in order to produce a flat model has been proven by Marshall Bern and Barry Hayes to be NP-complete. Further references and technical results are discussed in Part II of "Geometric Folding Algorithms". Some classical construction problems of geometry — namely trisecting an arbitrary angle or doubling the cube — are proven to be unsolvable using compass and straightedge, but can be solved using only a few paper folds. Paper fold strips can be