# Exploring the Times Table

Exploring the Times Table

The times table provides a rich source for mathematical discoveries. The plus table, on the other hand, is pretty dull. This Demonstration lets you explore both for comparison.

You can select which elements of the table will be shown or highlighted. Click the table's left border and top border to select (row and column) operands and the corresponding result. You can also click a result to select it and the corresponding operands. Deselect by clicking again or by clicking the top left-hand corner (in the operator position). The crosshairs highlight the selected row and column.

The diagonal can be highlighted to help emphasize the mirror symmetry of the table. In the times table, the diagonal contains the square numbers.

One observation about the times table is illustrated by highlighting the rectangle that contains 1 and that has the selected result in the lower right-hand corner. The area of this rectangle (its number of cells) equals the selected result. You do not need to know the results to play around with that rectangle. How many other such rectangles are there with the same area?

The "also highlight" control lets you highlight additional results, related to the selected result.

The slider labeled "modulo" highlights all cells equal to the selected result (or equal to 0, if no result is selected) modulo this slider's value. Slider value 0 disables it.