A climber sets out at 8 a.m. from sea-level, reaching his goal, a 2,000 metre peak, ten hours later. He camps at the summit and starts his return the next morning at 8 a.m. After a leisurely descent, he is back at sea-level ten hours later.

Is there some time of day at which his altitude is identical on both days? Try to answer this before reading on.

Continue reading ‘Brouwer’s Fixed-Point Theorem’

You must be logged in to post a comment.