making it both the birthplace and the proving ground of the Renaissance. Brunelleschi’s dome still rises from the terra-cotta sea of Florence’s roof tiles, itself terra-cotta clad yet ...

Some 50,000 people visit St. Peter’s Basilica in Vatican City daily. The 500-year-old structure, with its 448-foot-high dome, ...

But the Renaissance only revived the dome, essentially splitting the difference ... The mathematicians had begun with little knowledge of architecture, but they had a distinct advantage.