The speed of the athlete running down the runway is kinetic energy - the faster the athlete, the more kinetic energy and the higher they should be able to vault. Once the pole is planted, it bends, absorbs the kinetic energy and transfers it into potential energy in the pole.
The athlete uses the potential energy in the pole to lift themselves upwards towards the bar, a bit like a spring uncoiling. Once they approach the bar, they should have just enough kinetic energy to clear the bar and drop down to the mat.
Contrary to what many believe, vaulters don't use strength to lift themselves over the bar. Instead, it's about running as fast as possible without compromising technique (speed accounts for two-thirds of the height that can be gained) and then using the energy in the pole.
Interestingly, male vaulters are at about the limit of what they can achieve unless pole technology advances significantly or athletes can somehow run faster. In fact, Lavillenie's record is beyond what boffins thought was possible based solely on mathematics and it's part of the reason why it took 20 years for Sergey Bubka's record to be beaten - Bubka broke the record 17 times between 1984 (5.85m) and 1994 (6.14m).
Mathematicians believe the women's record, however, has the potential to advance significantly, given it is a relatively new event. Russia's Yelena Isinbayeva set the current record of 5.06m in 2009.
Eliza McCartney extended her New Zealand record to 4.80m last month and then placed fifth at the world indoor championships. She's an outside chance of a medal in Rio. The 19-year-old is one athlete who understands the science of what she does, considering she's studying for a Bachelor of Science in physiology.
"A lot of what I learn is relevant at training," she says. "It's like a practical after class."