河圖 · 洛書
兩張古圖
《繫辭傳》：「河出圖，洛出書，聖人則之。」 相傳河圖出自黃河的龍馬背上，伏羲看到它而畫出八卦； 洛書出自洛水的神龜背上，大禹看到它而制定九疇。
神話歸神話，考古上河圖洛書的圖形最早出現在宋朝，屬陳摶、邵雍一系； 但《繫辭傳》在戰國至漢初已提到這兩個名稱，所以至少那時就已經有數圖對應卦象的觀念。
這兩張圖在易經體系裡的主要功能，是把抽象的陰陽、五行、八卦，落到具體的數字排列上， 讓哲學變成可計算的結構。
The Xici Zhuan says: “The Yellow River produced the diagram, the Luo River produced the book, and the sages took these as their model.” Mythologically, the Hetu was carried on a dragon-horse from the Yellow River and seen by Fuxi, who derived the trigrams from it; the Luoshu was carried on a divine turtle from the Luo River and seen by King Yu, who used it to organize governance. Archaeologically, the diagrams as we know them appear in Song-dynasty sources, from Chen Tuan and Shao Yong, but the Xici Zhuan already mentions their names in the late Warring States to early Han, so the concept of number-diagrams matched to hexagram structure goes back at least that far.
河圖
十個數字排成五個位置，每個位置一陰一陽配對：
- 北（下）：1（陽）+ 6（陰）= 水 · North (below): 1 (yang) + 6 (yin) = Water
- 南（上）：2（陰）+ 7（陽）= 火 · South (above): 2 (yin) + 7 (yang) = Fire
- 東（左）：3（陽）+ 8（陰）= 木 · East (left): 3 (yang) + 8 (yin) = Wood
- 西（右）：4（陰）+ 9（陽）= 金 · West (right): 4 (yin) + 9 (yang) = Metal
- 中：5（陽）+ 10（陰）= 土 · Center: 5 (yang) + 10 (yin) = Earth
奇數，也就是一、三、五、七、九，為陽，畫成實心黑點；偶數，也就是二、四、六、八、十，為陰，畫成空心圈。 每對數字之差都是五，象徵中央的五是五行的樞紐。
河圖推出先天八卦，也就是伏羲方位，用來講體，也就是宇宙本來的結構， 和後面要說的洛書、後天八卦互相對照。
Ten numbers sit in five paired positions; each pair differs by 5. Odd numbers, shown as filled dots, are yang; even numbers, shown as open circles, are yin. The Hetu generates the Xiantian Bagua, the Fuxi arrangement: the structural, essence-level reading of the cosmos.
洛書
九個數字排成三乘三方格，每一行、每一列、兩條對角線相加都等於十五：
4 9 2 3 5 7 8 1 6
這是世界上最早的已知幻方。中間是五，代表土，也代表中央。 九個數字以中央為樞紐旋轉。
洛書推出後天八卦，也就是文王方位，用來講用，也就是宇宙在時間中運作的結構。 占卜、風水、奇門多半使用這套系統。
Nine numbers sit in a 3-by-3 grid; every row, column, and diagonal sums to 15. This is the world's earliest known magic square. The Luoshu generates the Houtian Bagua, the King Wen arrangement: the operational, function-level reading of the cosmos. Most divination, fengshui, and qimen practice uses this system.
先天與後天
兩個八卦排列方式，是易經體系的核心內部區分：
- 先天八卦（伏羲方位）：講體。對立卦在對立方位，乾在上、坤在下、離在東、坎在西， 這是完美對稱、靜態的圖。
- 後天八卦（文王方位）：講用。八卦按時令、五行排列，震在東屬春、離在南屬夏、 兌在西屬秋、坎在北屬冬，這是在時間中流動的圖。
學易經時，先讀先天抓結構，再用後天讀變化。 命理、風水、占卜大多在後天體系裡操作，先天則是背景的邏輯。
Two trigram arrangements form a core internal distinction in the Yijing. The Xiantian (innate, Fuxi) arrangement is symmetric and static, pure structure: Qian at the top, Kun at the bottom, Li in the east, Kan in the west. The Houtian (operational, King Wen) arrangement is organized by season and phase: Zhen in the east for spring, Li in the south for summer, Dui in the west for autumn, Kan in the north for winter. Study the Xiantian to grasp structure; use the Houtian to read change. Most divination, fengshui, and astrology operate within the Houtian framework.
現實操作
對大多數用戶而言，河圖、洛書、先天、後天都是背景知識，知道它們存在、知道八卦有兩種排列，就已經足夠。 除非進入專業領域，例如風水、奇門、紫微，否則不需要把河圖洛書的數字排列背熟。
但知道這個體系之後，讀古典文獻不會卡住，看到「先天八卦」「後天八卦」「五行之數」「九宮」這些詞， 會立刻知道它們在講什麼。
For most users, the Hetu, Luoshu, Xiantian, and Houtian are background knowledge: knowing they exist, and that bagua has two arrangements, is enough. You don't need to memorize the number layouts unless you are entering a specialized practice such as fengshui, qimen, or ziwei. But having the framework means classical texts no longer stall you: seeing terms like Xiantian Bagua, Houtian Bagua, the numbers of the five phases, or the nine palaces, you will immediately know what they mean.