In order to answer this question, one needs some back story....

There exists mathematic patterns in nature (the macrocosmic) that we (the microcosmic) conform to! If this sounds goofy, please consult Chapter 2 of my book, The Complete Idiot's Guide to Feng Shui . Many examples are provided regarding the Fibonacci Sequence, the Golden Ratio, and Pi.

As an example, let's take the Fibonacci Sequence (0,1,1,2,3,5,8,13,21...). This is a sequence of numbers in which each number in the series is the sum of the two previous numbers. For example, 3 + 5 = 8; 5 + 8 = 13, and so forth to infinity. You can find the Fibonacci Seqence on many flowers. The number of petals is a Fibonacci number: buttercups 5; lily and iris, 3; daisies, 8,13, 21, 34, 55 or 89. We all have Fibonacci fingers: 2 hands, each of which has 5 fingers broken up into 3 parts of 2 knuckles. In fact, please know that feng shui's fundamental principles correspond to the numbers of the Fibonacci Sequence: Yin and Yang (2), the Luoshu (3), Five Phases (5), and Eight Trigrams (8). To sum up, the Fibonacci Sequence, the Golden Ratio and Pi are examples of mathematical patterns found in nature and our bodies. They have influenced art, architecture, and music.

The ancient Chinese recognized these patterns in nature and recorded their findings in the Zhouyi. Now, what's the Zhouyi you ask? During the Han dynasty (206 BC - AD 220) scholars set about collecting the great texts of their culture. Before the Han dynasty the Yijing (I Ching/Book of Changes) was known as the Zhouyi, a oracle of all cosmic and human conditions. Commentaries called the Ten Wings were attached to the Zhouyi and the new compilation was called the Yijing. The origin of the Zhouyi remains a mystery. Modern scholars believe it was most likely an accumulative text written by many people. Although the mythical sage-king Fuxi, King Wen (the founder of the Zhou dynasty) and his son the Duke of Zhou are often credited with writing the Zhouyi, there is no proof.

Anyway, the ancients recorded their observations of nature symbolically in the form of solid (yang) and brokin (yin) lines. However, in 1980, a scholar named Zhang Zhengland discovered that the lines of the trigrams and hexagrams were actually not part of the Zhouyi. Oracle bones and bronze sacrificial containers dating from 1500 - 1000 BC record trigrams and hexagrams in numeric form, proving that originally, the Zhouyi/Yijing was based on numerological divination. Zhengland theorized that over time the odd numbers became the solid yang lines; even numbers, the broken yin lines as we now know them.

The classical system of Flying Star (or The Nine Floating Stars) is a mathematical system. There are two specific mathematical diagrams of the universe. One is the Hetu or Yellow River Map. This is a pattern of black (yin) and white (yang) dots purportedly found on a dragon-horse emerging from the Yellow River. The Hetu symbolizes the ideal, perfect, and sedentary world.

The Luoshu, also known as the Luo River Writing, is a pattern of black (yin) and white (yang) dots said to be found inscribed on a turtle's shell. The Luoshu correlates to the After Heaven Sequence of trigrams (conceivable as early as the Han dynasty 206 BC - AD 22) denoting motion, transformation, and interaction of natural and human qi. Now, we all know these two diagrams couldn't have appeared on the backs of animals. The fact is, their origins are unknown.

Just like the Hetu, the Luoshu's dots correspond to a number. Numerically, the pattern is thus:

The Luoshu is also known as the Magic Square of Three. This is because three numbers add up to 15 along any diagonal, vertical, or horizontal line. In the early Warring States period (475 - 221 BC), the principle of the five phases, the 8 trigrams, and the Luoshu correlated into one system. We call this the bagua (a nine-celled grid).

Like the After Heaven trigram sequence, the Luoshu diagram moves, symbolizing a world of constant transformation. Although the nine-celled bagua is square, it is inherently cyclic. First, connect the two pairs of odd (yang) numbers 1 and 9, and 3 and 7. Then, draw a line through the cells 6 and 1, 8 and 3, 4 and 9, and 2 and 7. The end result should look like a counterclockwise swastika (not to be confused with the clockwise symbol used by Hitler's Third Reich.)

The swastika moves in a counterclockwise fashion because it expresses future time. The clockwise movement expresses passing time. Richard Wilhelm in his preface to the I Ching (1950) explains it this way: "The usual clockwise movement, cumulative and expanding as time goes one, determines the events that are passing; an opposite, backward movement, folding up and contracting as time goes, through which the seeds of the future take form. To know this movement is to know the future. In figurative terms, if we understand how a tree is contracted into a seed, we understand the future unfolding of the seed into a tree."

Feng shui is concerned with predicting the probability of future events. Please know the Chinese are concerned with acausal probabilities, chance happenings and coincidences that are connected by seemingly unrelated events. They believe human events are not necessarily caused by natural phenomena, only connected in an acausal relationship. Countless hours through countless centuries were spend correlating acausal events between the macrocosmic world and our well-being (again, the microcosmic). Numbers became a method of recording and predicting.

(By the way, this acuasal theory is called synchronicity, a word coined by Carl Jung.)

Each number of the bagua reflects a certain kind of qi. It's important to understand (following the law of yin and yang) that no number can be favorable all the time. Rather, its favorability is cyclic. That said, in Flying Star, one moves the numbers around the bagua in a specific sequence. Numbers and time go hand-in-hand. The 20-year cycle your home 'was born into', the annual year, and you're home's trigram are all significant. The number configuration within each cell can help predict likely events. These events can either be discouraged or encouraged by the placement of one of the five phases. Remember, the five phases, the luoshu numbers, directions, and trigrams were correlated. So, for example, South is associated with the Li trigram, the color red, and the number 9.

In conclusion, the Luoshu describes the workings of the universe. A feng shui master seeks to study these numbers to change the course of human destiny.