TED-ED: How the K_nigsberg bridge problem changed mathematics - Dan Van der Vieren

The video explores the famous mathematical problem of the seven bridges of Konigsberg, a city divided by the Pregel River with two islands connected by seven bridges. Carl Ehler's curiosity about crossing all bridges without repetition led him to seek help from Leonhard Euler. Euler initially dismissed the problem but later developed graph theory to solve it. He discovered that a path crossing each bridge once is impossible due to the odd degree of nodes. Euler's work laid the foundation for graph theory, explaining Eulerian paths and circuits. The video also touches on historical events that altered Konigsberg, now Kaliningrad, and the lasting impact of this mathematical riddle.

What was the main question Carl Gottlieb Ehler was trying to solve about the bridges of Konigsberg?

• How to connect the islands with a single bridge

• How to cross all seven bridges without repeating any

• How to remove the bridges to simplify travel

• How to build more bridges in the city

What was Euler's initial reaction to the bridge problem posed by Ehler?

• He solved it instantly without any effort

• He thought it was a simple geometry problem

• He dismissed it as irrelevant to mathematics

• He immediately saw its mathematical significance

In Euler's simplified graph of Konigsberg, what does each node represent?

• A bridge

• A river

• A city

• A landmass

Under what condition is a Eulerian path possible according to Euler's theory?

• When all nodes have the same degree

• When there are no nodes of even degree

• When all nodes have an odd degree

• When there are exactly two nodes of odd degree

What historical event inadvertently created a Eulerian path in Konigsberg?

• The destruction of two bridges during World War II

• The construction of additional bridges

• The removal of all bridges by the Soviet Air Force

• The rebuilding of the city as Kaliningrad