  A new, geometric and easy to understand approach to finite population
sampling is presented. In this approach, first-order inclusion probabilities
(FIPs) are represented by bars in a two-dimensional coordinate system, and
their different arrangements lead to different designs. Only based on the
geometric approach, designs can be fully implemented, without the need for
mathematical algorithms. An special arrangement of the bars, is equivalent to
Madow 1949 systematic method, which easily, with rearranging the bars, while
keeping the FIPs unchanged, results in different second-order inclusion
probabilities (SIPs) equivalent to other famous finite population sampling
designs, such as Poisson sampling, maximum entropy sampling, etc. Geometric
visualization of sampling designs leads to increased creativity of researchers
to provide new efficient designs. This approach opens a new gate to finite
population sampling that can deal with problems such as optimal designs,
implementation of maximum entropy sampling, etc.
