It doesn’t take a genius to know that accidents cause traffic jams. But it did take a genius to figure out why sometimes rush-hour traffic slows to a bewildering stop for no apparent reason at all.

In the last few months, two mathematicians at the University of Exeter in England came up with this equation, which has become something of a validation for engineers urging new approaches to traffic management. It’s changing things in Houston already.

Rice University’s Rolf Ryham explains the man.

He said for the first time, this equation takes driver “reaction time” into account. What’s revealed here could hold the key to solving Houston’s traffic problems.

Basically it’s mathematical proof that on a crowded freeway, when one driver just taps on his brakes, the driver behind him reacts and brakes a little more. The driver behind him brakes even more, and so on until drivers actually stop moving. It’s the kind of jam that happens on 290 every day.

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“Slowing traffic down a little bit during peak periods is OK,” Highway 290 Expansion spokesman Stephen Hrncir said. “It’s the near-stop conditions we need to avoid.”

It’s called “cascading.” You can see it by speeding up video of 290 at rush hour. There are waves of congestion moving backward. The ripples start when someone up front does something that causes drivers behind him to brake, starting a cascade of slowing traffic.

“A few minutes ago someone may have moved lanes or done something to slow down a little bit and that’ll cause things to slow down or stop,” Ryham said. “And you’ll run into that, and you’ll be like, ‘where did this come from?’ There’s no cops or anything.’”

This is the kind of traffic that engineers think about: When cars are very close together, but they are moving. That’s when one small problem, someone changing a radio station or being on their cell phone, can create a traffic backup that seems to have no explanation.

“The last car that stopped may have stopped after the last car started moving again,’ Hrncir said. “But now his stop can be the next intersection back, and he still is causing cars behind him to stop so that’s the cascade effect.”

So when crews break ground on the new 290 in three years, they’ll be building it to minimize the cascade effect. There will be left shoulders; special entrance and exit lanes; even hills will be less steep.

“The higher the grade as you drive the street, they tend to be uncomfortable about what might be on the other side,” Hrncir said. We’re using grades of 2 to 3 percent; historically, we would have used much higher grades.”

It’s all to get around what is now a mathematical truth.

“This is a feature which will consistently show up in traffic; there is no way around it,” Ryham said.

One that a $4 billion, 17-year construction project may eventually bypass, at least on Highway 290.