Measuring a surface by a cubit

Brief

This lesson asks you to measure area with non-standard units and to explain how gaps and overlaps change the result. The museum offers a text that defines an area as a cubit by a cubit; the record has nothing on gaps and overlaps. Covering real surfaces with tiles, and the gaps and overlaps that appear, are the class's own work. ¹

What does a surface need before you can count its area?

Cover a sheet of paper with square tiles of the same size. Leave no gaps and no overlaps. Then leave a gap and count again. What changes?

Go deeper

Al-Khwarizmi gave measuring a chapter of his Book of al-Jabr and al-Muqabala. The chapter opens by saying that "one by one" means an area, that is, a cubit by a cubit ². In the preface he lists the measurement of land among the needs he wrote the book for ³. So the record on mensuration shows what is measured (an area), in what unit (a cubit by a cubit), and a need it served (land).

Think about it

Al-Khwarizmi counts an area as a cubit by a cubit and lists the measurement of land among his book's needs. Why might someone who owns land want its area told as a number of squares of one size, and not as "about this big"?

Into the museum

Mensuration: what is measured, and in what unit, in al-Khwarizmi's chapter.
Al-Khwarizmi: the author of the book in which the chapter appears.

Try this

Read the record on mensuration. Cover a sheet of paper with square tiles and count them. Then try tiles with half the side and compare the counts.