Climb 1 m north first, and then climb 2 meters south-equivalent to going south from home 1 m. Finally, climbing eastward | (yes 1) meters is equivalent to going south from home 1 meter, and then going east 1 meter. It is equal to an isosceles right triangle with a base angle of 45. That is, I am now in the southeast (45 east of south).

If the ant starts to climb one meter north, and his home is in his south, but he climbs two meters south in turn, then now his home is in his north, and finally he climbs one meter east, so his home is in his northwest. It is just in the northwest, with a 45-degree angle from north to south and from east to west.

Extended knowledge

It's as close as two roads for a small ant to go home, because the two roads are the same length. Method 1: Count the squares. When a small ant goes home from the diagonal, a * * will pass through 16 squares, and when it goes home from the right angle, it will pass through 16 squares.

Method 2: Translation: Move the vertical grid of the small ant from the diagonal home page to the left, which is completely coincident with the right-angled edge on the left, and move the horizontal grid downward, which is completely coincident with the right-angled edge below. Therefore, the distance for the little ants to go home by two routes is the same.

Method one. Transforming thinking in solving mathematical problems refers to changing the direction of the problem from one form to another from different angles when encountering obstacles in the process of solving problems, in order to seek the best way to make the problem simpler and clearer.

Mathematical thinking: reverse thinking, also called divergent thinking, is a way of thinking about common things or ideas that seem to have been stereotyped. Dare to think in the opposite direction, let thinking develop in the opposite direction, explore deeply from the opposite side of the problem, establish new ideas and create new images.

Logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, generalize, judge and reason things with the help of concepts, judgments and reasoning in the process of cognition. Logical thinking is widely used to solve logical reasoning problems.

Innovative thinking refers to the thinking process of solving problems with novel and original methods. Through this kind of thinking, we can break through the boundaries of conventional thinking, think about problems with unconventional or even unconventional methods and perspectives, and come up with different solutions, which can be roughly divided into four types: difference, exploration, optimization and negation.