October 29 in History

Cyrus the Great walked into Babylon in 539 BCE without a battle. The priests had opened the gates for him — they hated their own king. He immediately issued a decree allowing exiled peoples to return home, including the Jews who'd been captive for 50 years. The cylinder he inscribed is now in the British Museum. Some call it the first human rights charter. Cyrus didn't conquer Babylon. He was invited in.

Constantine entered Rome in 312 after defeating Maxentius at the Milvian Bridge, where his rival drowned in the Tiber wearing full armor. Soldiers fished out the body, cut off the head, and paraded it through the streets on a pike. Constantine claimed he'd seen a cross in the sky before the battle with the words "In this sign, conquer." He'd been outnumbered two to one. Within a year, he legalized Christianity across the empire.

Valentinian III was six years old when he became Western Emperor. Licinia Eudoxia was probably around the same age. The marriage united the two halves of the Roman Empire through the House of Theodosius. Valentinian would rule for 30 years. The Western Empire would fall 21 years after his death. The dynasty ended with him.

Conradin was 16 years old. He'd marched to Italy to reclaim his grandfather's throne. Charles I of Sicily captured him after battle, tried him for invading, and beheaded him in Naples. The crowd watched the last Hohenstaufen emperor die on a scaffold. With him went the dynasty that had ruled Germany for 138 years. No legitimate heir remained.

Dutch warships smashed the Swedish fleet in 1658 in a strait so narrow the battle was named for the sound of cannon fire echoing off both coastlines. The Dutch were defending Denmark, their trading partner. Sweden had marched across frozen sea ice that winter to invade Copenhagen — the Baltic had turned into a highway. Thirty Swedish ships went down. The Dutch lost one. Sweden's dream of controlling all Baltic trade sank with them.

Portuguese forces decapitated King António I on the battlefield. They sent his head to Luanda as proof. The Kingdom of Kongo never fully recovered. Portuguese control over the region tightened. Within decades, the kingdom that had traded with Europe as an equal became a source for enslaved people. The battle ended Kongo's independence.

Leibniz needed a symbol for summation in his new calculus. He chose the long s—basically an elongated letter that looked like ∫. It stood for "summa." Newton had developed calculus independently using different notation. Leibniz published first. His symbols won. Every integral you've ever seen uses the mark he picked on this day.

Lt. William Broughton spotted a snow-covered peak from the Columbia River and named it for British Admiral Alexander Arthur Hood, who'd never seen the Pacific. The Multnomah people had called it Wy'east for centuries. Hood is an active volcano. Its last major eruption was in the 1790s, right around when Broughton sailed by. It's overdue.

Union forces repelled a Confederate night attack at Wauhatchie, Tennessee, securing the "Cracker Line" supply route into besieged Chattanooga. Breaking the Confederate stranglehold on supplies saved the starving Union garrison and enabled the decisive victories at Lookout Mountain and Missionary Ridge that followed weeks later.