3 veg on same ground

My other half has heard somewhere about growing 3 different types of veg together if space is limited. Apparently first you plant sweetcorn..which runner beans then climb up and lastly courgettes are planted around the base to shade all the roots. Is this a well known idea? Has anyone else tried the method and if so what were the results like? he's determined to give it a go but I said I'd run it past folks on this site who may have more knowledge/ experience.
I'm interested to hear anyones views.

 

I believe that this is an American Indian practice known as the Three Sisters (corn, beans, squash). Quite a few sites on this if you google.

 

Further to this, has anyone got some tips on other parallel plantings? I have a fairly small veg plot and need to maximise my planting. For instance, I have a short single row of potatoes: could I get away with planting a row of broad beans either side of the spuds? I presume that the beans will have finished before I dig maincrop potatoes?