In geometry, the intersecting of two objects is usually "smaller" or equal to a larger object. All non-two-dimensional objects are assumed to lie within a certain "common space", except in complex set theory, where the intersecting of arbitrary collections is explicitly defined. In geometric intuition, however, there is no such thing as an "intersection", and therefore no such thing as a "geometric intuition". The intersection in this case is simply one of the basic concepts of geometric geometry. If there were such a thing as an intersection in geometry, then all the various geometric intuitionistic notions that we have discussed would be incomplete.
In simple terms, an intersection can be defined as the area in a plane that touches at least one of its sides. The angles in the shape must also be given, since one cannot "conceive" of any shape without angles.
One can think of the "triangle of unity" as being like the "intersecting" of any three shapes. The difference between this and the geometry is that the intersection only has to "touch" at least one of the sides, while the three shapes can have more than one side. The angle of the triangle is the distance from the center of the triangle, and it is called this angle because it is equal to the angle of the triangle of unity. This is important because this ratio shows us that the three triangles are lying along the same line, which is called the "diagonal line". Therefore, a triangle can be considered to be the intersection between three different shapes, while a polygon can be considered the union of four or more shapes.
It will also help if we consider an intersection to be "contained" within a circle. That is, if a triangle is inside a circle, then so is an intersection. If we have four circles with four different points, then the intersection between any two of these circles is going to be inside of another circle.
Intersections do not necessarily have to be equidistant. They can be either. If we consider a straight line from one point to another point, it is called an "intersection", and if the two lines meet at an angle of ninety degrees, it is known as a "right angle". In geometric intuition, these two shapes are the same and can be treated as being of the same size. In complex number theory, though, a circle has no size but still can be considered an intersection. if there are fewer points than edges, and one edge is a right angle.
There are many different ways to define the intersecting of three or more sets of objects. However, the most fundamental way is the same, and that is to say that there is always a "common space".