Level Curves

Level curves are lines on a map or graph that connect points with the same value of a function, such as elevation, temperature, or pressure. Imagine a topographic map where each line connects areas of equal height; these are level curves or contour lines. They help visualize how the function changes across space without showing every detail. Closely spaced lines indicate a steep change, while widely spaced lines show a gentle slope. Level curves are useful in various fields like geography, meteorology, and engineering for understanding patterns and variations within a given system.