I was interested to read about research into falling over (25 December 2004, p 48). There is a way to reduce your chances of tripping and slipping while walking: change the way you walk.
Most people I have observed (and, I suspect, the majority of westerners) walk by "controlled falling". That is, they pitch their bodies forward so that their centre of gravity is heading for a point ahead of their front foot, and their back foot then has to move forward in time to stop them falling. Hence, if the back foot is stopped from coming forward they fall on their face. Similarly if the foot does arrive on time but lands on a slippery surface, the foot slips forward and they fall.
In t'ai chi walking, the centre of gravity of the body is always moving towards a point over the front foot. When the weight has come off the back foot it moves forward and the foot is placed down without yet supporting the body's weight. If the back foot is stopped, the weight carries on down into the other foot, so instead of tripping you just dip down onto the front foot. It takes most adults quite a bit of practice to learn how to do this without thinking, but once you do it is a very relaxed and efficient way of walking.
T'ai chi has been shown to be very effective at reducing falls in the elderly. It also strengthens leg muscles, which, as the article states, helps you to avoid falling over.
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