The two points in question will be different distances from the observer and the illusion of parallax is caused by the fact that vision, like light, follows straight lines. When the observer views the nearer point, The line of his vision toward that point is at a given angle within the full arc of his vision. For example let us say that the view straight ahead is zero degrees, and one point, nearer the observer, is at minus five degrees while a point which is farther away is at minus two degrees. The apparent angular distance between the points is a subjective three degrees to the viewer. If the viewer moves ten meters to his right, the angular direction to the nearer object, as it is on a shorter radius, will change more than the angular direction to the farther object. So, for instance, when the angular direction to the nearer object is at minus ten degrees, the father object may only have moved to minus three degrees. Now the subjective angular difference in position is seven degrees. The objects appear to have moved relative to each other.
On a macro scale, this effect is responsible for the fact that, in a moving car, one can look at distant mountains and see them seem to move (retard) in position beneath a seeminly motionless moon. The moon is at such a distance that the subjective angular change in position relative to an earth-bound observer is extremely slight, even as many miles are covered. The mountains, much closer, exhibit a much greater seeming change in angular position.
On a galactic scale, parallax created by the different orbital positions of the earth causes the stars to seem to move. Measurements in parallax as the earth goes through its orbit was the first reliable way to determine the distances to the closest stars. This method was first used by Friedrich Wilhelm Bessel in 1838 when he measured the distance to 61 Cygni, and it remains the standard for calibrating other measurement methods (after the size of the orbit or the earth is measured by radar reflection on other planets). In 1989, a satellite called "Hipparcos" was launched with the main purpose of obtaining parallaxes and [proper motions]? of nearby stars, increasing the reach of the method ten-fold.
On a micro scale, the thickness of a ruler can create parallax in fine measurements. One is always cautioned in science classes to "avoid parallax." By this it is meant that one should always take measurements with one's eye on a line directly perpendicular to the ruler, so that the thickness of the ruler does not create error in positioning for fine measurements.
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