An­cient math wiz sired ‘Hill­billy toy’

Northwest Arkansas Democrat-Gazette - - STYLE -

Tourists look at a do-noth­ing and think, “Why not?” Then they buy it as a sou­venir of won­der­ful Arkansas. But they should ask, “Why”?

Be­cause there’s a rea­son why.

“I was at a party with a his­tory pro­fes­sor and he had one of these,” Sam Lawhorn says, hold­ing the toy in ques­tion — a wooden square fit­ted with a han­dle at­tached to two slid­ers on per­pen­dic­u­lar, in­ter­sect­ing grooves. “Hill­billy En­ter­tain­ment Cen­ter” is stamped in a cor­ner.

As he turns the han­dle, the slid­ers move back and forth in their grooves with­out col­lid­ing. Mean­while, the end of the han­dle trav­els around the block, on the same path ev­ery time.

“I picked it up and I said, ‘Whose Archimedean tram­mel is this?’”

Lawhorn sets the toy on a glossy ta­ble in the math­e­mat­ics depart­ment at the Univer­sity of Arkansas at Lit­tle Rock, where he re­cently earned a bach­e­lor’s de­gree in math. He taps the end of the crank and ex­plains that the path is a true el­lipse.

“That’s what this was orig­i­nally de­signed for in 250 B.C. by Archimedes of Syra­cuse,” Lawhorn says.

The Greek math­e­ma­ti­cian is best known for (sup­pos­edly) leap­ing naked from the bath and run­ning down the street while shout­ing, “Eureka!” Be­cause he’d thought of a use­ful ap­pli­ca­tion for wa­ter dis­place­ment.

He’s also cred­ited with a pile of in­ven­tions, from an ef­fi­cient pump (the Archimedean screw) to the com­pound pul­ley and the odome­ter; to pos­si­bly apoc­ryphal ma­rine weapons, in­clud­ing a big iron hand on a long pole. He def­i­nitely made dis­cov­er­ies about circles (in­clud­ing a nu­mer­i­cal value for pi) and used the ad­vanced math now called cal­cu­lus.

With a hand­ful of as­sis­tants and the fruits of his mind, he kept the Ro­man army and navy out of Syra­cuse for years. Lawhorn mar­vels: “This was Gen. Mar­cus Claudius Mar­cel­lus, who was known to be a great Ro­man gen­eral, and he’s deal­ing with this an­noy­ing math­e­ma­ti­cian.”

Even­tu­ally the Ro­mans over­ran the Si­cil­ian city and a sol­dier stabbed el­derly Archimedes to death. In one story, the ge­nius is so ab­sorbed in work­ing a prob­lem he re­fuses to leave it and go with the sol­dier to Mar­cel­lus; in an­other the sol­dier mis­takes his pointy draft­ing tools for weapons.

The el­lipse, or stretched cir­cle, is use­ful in ar­chi­tec­ture, en­gi­neer­ing and in cal­cu­lat­ing the tra­jec­to­ries of pro­jec­tiles, and it is not easy to draw free­hand. Be­ing able to draw true el­lipses is also use­ful for draw­ing in per­spec­tive and cal­cu­lat­ing the or­bits of plan­ets.

— Celia Storey

Demo­crat-Gazette il­lus­tra­tion/CELIA STOREY

The “do-noth­ing” is a toy ver­sion of a draft­ing tool de­signed to draw el­lipses.

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