Triangle eating is not about McDonald's 三角パイ, nor is it about a food pyramid-style nutritional scheme. 三角食べ is all about the order in which you eat your food.
As the pictures show (and the text attests), the correct way to eat a meal is to start with your rice and work your way around bite by bite. One bite of rice, one sip of soup, one bite of your おかずor 飯. A lot of you may know this already, or have heard about this, but it would be a mistake to write it off. It's a big, big part of Japanese culture.
How big, you ask? Well, since the 1970s, Japanese schools have incorporated it into school lunches, like a part of the curriculum. And although expert testimony (W. M. Edgar, D. M. O'Mullane (9 1990). Saliva and oral health. British Dental Journal) from around the world supports the idea that interspersing sips of soup is good for keeping your mouth well salivated and therefore helping the digestion process.
But the reason for eating like this is not a nutritional one. It's part of the Japanese reverence for food that is one of the main reasons I love Japan. "和食をおいしく味わうため," according to wikipedia. Gotta love the classic wikipedia objectivity, especially in lines like this as well: 日本以外ではこのような概念はない。
If you want to try it out for yourself, remember, start with your rice, and try to size your bites so that you finish each portion of your meal at the same time.