“Bombshell: The Hedy Lamarr Story” is a documentary about a woman who may have been too beautiful for her own good.

Lamarr — who was born Hedwig Eva Maria Kiesler to a Jewish family in Vienna— made her bones by showing her bones — and the rest of her — in a 1933 Czech film called “Ecstasy.”

The film was a revelation. Pun intended. Running naked through the woods and swimming, simulating orgasm, it made her — just 18 years old when she filmed it — an immediate international sensation.

But while she is mostly remembered as a silver screen sex symbol, Hedy was more than just a pretty face. She invented an early version of spread spectrum communications, a technique of frequency hopping integral to modern communications technology, including cell phones and GPS.

This intellectual side of Hedy’s life was not a secret; Pulitzer Prize-winner Richard Rhodes wrote about it in 2011 in “Hedy’s Folly: The Life and Breakthrough Inventions of Hedy Lamarr.” But this television exposure (once again, pun intended) will reveal this side of her to a far wider audience.

At first glance it appears that Hedy was destined to live a storybook life. Her beauty landed her early film roles and marriage. She was still a teenager when she married Fritz Mandl, one of the wealthiest men in Austria, a Jewish arms dealer who cavorted with and sold weapons to Mussolini and Hitler.

The marriage turned out to be unhappy.

Hedy fled it, literally, disguising herself as the maid and sewing all her jewelry into the lining of her coat. From there she went to Paris, where she met Louis B. Mayer, who brought her to the United States and cast her in a string of successful films opposite some of the biggest names in the film biz: Charles Boyer, Spencer Tracy, and Clark Gable, to name just three.

She became the model for Disney’s Snow White and the comic books’ Cat Woman. She so moved Mel Brooks that he named the Harvey Korman character in “Blazing Saddles” after her — Hedley Lamarr.

In 1941, Hedy Lamarr stars in “Ziegfeld Girl.” (Everett Collection)

But Hedy Lamarr, far from the stereotypical Hollywood airhead, didn’t let the acclaim go to her head. “Any girl can be glamorous,” she said. “All you have to do is stand still and look stupid.”

Hedy didn’t stand still. “Bombshell” makes great use of recently uncovered audio tape in which Lamarr talks about her life in a way that makes clear how self-aware and smart she really was.

Though she had no technical training, she seemed able to visualize solutions to problems some people didn’t even know existed. Imagining the way birds fly, she convinced buddy Howard Hughes that planes should do away with the traditional design, in which wings are perpendicular to the frame. She argued they should be swept back, which is the standard form today.

She also created a bullion-like cube; when you put it in water it would produce a Coca-Cola-like drink. “One of my boo-boos,” she acknowledges.

Another invention, noted in Rhodes’ book but not in the film — she also created a tissue box attachment for disposing of used tissues.

Her breakthrough was for a guidance system to control torpedoes after they leave a submarine. At the time, torpedoes were directed via a radio signal that the enemy easily could jam. Her thought was to create a way for the frequencies to be changed simultaneously in the torpedo and in the guidance system on the sub.

She worked with composer George Antheil to bring the idea to fruition; the two ultimately shared the patent. Though it is not entirely clear why, the Navy rejected the idea. Perhaps it was too far ahead of its time. Ultimately, it became the basis for secure WiFi, GPS, and Bluetooth, though by the time that happened Hedy’s patents were expired and she no longer could sue for recompense.

It takes something of a leap of faith to believe that the mind that created a used-tissue holder also came up with an idea as sophisticated as a frequency modulator. One train of thought is that she overheard some discussion on the subject over dinner at the Mandl house, where Nazi scientists were frequent guests.

Certainly it would be nice to credit Hedy, if only because the fairy tale that was her early years went bad. She ultimately married six times, saying, “I must quit marrying men who feel inferior to me. Somewhere there must be a man who could be my husband and not feel inferior. I need a superior, inferior man.”

She never found him. Unfortunately, in her later years Hedy became a virtual recluse, going through a series of poorly executed plastic surgeries. Also, her money ran out.

Sadly, there was no fairy tale ending here.

“Bombshell” is a worthy addition to the PBS American Masters series, a fascinating look at a woman for whom physical beauty was not enough. It airs on PBS May 18 at 9 p.m. (Best to check local listings.)