Mathematics students often encounter confusion when distinguishing between rational and irrational numbers. However, mastering this fundamental concept becomes straightforward once you understand the ...

When you hear the words "rational" and "irrational," they might bring to mind the relentlessly analytical Spock in "Star Trek." If you're a mathematician, however, you probably think of ratios between ...

In this chapter, we look beyond the whole numbers at other numbers that are included in school mathematics in grades pre-K to 8, particularly in the upper grades. We first look at the rational numbers ...

When my students grow too dependent on their calculators, I ask them to find a number that, when multiplied by itself, gives them 2. Students quickly see that since 1² = 1 and 2² = 4, the answer has ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

The ancient scholar Hippasus of Metapontum was punished with death for his discovery of irrational numbers—or at least that’s the legend. What actually happened in the fifth century B.C.E. is far from ...