The?Nine?square Problem is used as a?pedagogical tool in the introduction of architecture to new students. Working within the problem the student begins to discover and understand the elements of architecture. Grid, frame, post, beam, panel, center, periphery, field, edge, line, plane, volume, extension, compression, tension, shear, etc. The student begins to probe the meaning of plan, elevation, section and details. He learns to draw. He begins to comprehend the relationships between two dimensional drawings, axonometric projections, and three dimensional (model) form. The student studies and draws his scheme in plan and in axonometric, and searches out the three-dimensional implications in the model. An understanding of the elements is revealed, an idea of fabrication emerges.

The Nine square Problem

Build a model at ?”=1’–0 scale of the following. Make a 30/60 isometric drawing in pencil on tracing vellum of the following. The constructed model and the drawing will be the basic working tools for the research and study of the Nine square problem.

Columns – white, base board – black, panels – gray. One grid 15’ divided into 5’s and 3’s. One grid 16’ divided into 1’s and 2’s.

The nine square falls between two poles, one of complete fluidity and one of complete containment.

The idea of The center and the periphery. 1 center cell and 8 peripheral cells.

Take the full panels (model) and study spatial relationships within the 9 square grid (16 columns). Then take the scheme and drew up in pencil in axonometric. This form of study will be carried in through the following problems.

1. Full panels.

2. ? Panels (Horizontal/Vertical).

3. Combine Full and Half Panels.

4. Curved Panels and half Circle.

5. Combine Full and Curved Panels.

6. Combine Full, Half, and Curved Panels.

7. Full Panel at 45°or 60°. Or, 45°and 60°.

8. Combine Full Panels 90°and 45°or 60°。

9. Combine Full (90°,60°,45°) ?, and Curved Panels.

10. Above systems off the column frame (not touching columns).

11. Make series of volumes (circle, square, triangle) ranging from 1’ square, 1’ diameter, 1’ triangular to 10’ square, etc. and ranging from 1’ vertical height to 10’ vertical height.

12. Combine columns with panels in a series of different combinations.

13. Build stairs, ramps, straight run stair, U run stair, circular stair, straight run ramp, U run ramp.

14. Build second storey frame and continue study.

15. Build third storey frame and continue study.

16. Build roof structures ? circle, ? lozenge or ? diamond, ? square.

17. Combine all systems.

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九宮格問題被用作向新生介紹建筑學(xué)的教學(xué)工具。在（九宮格）問題中，學(xué)生開始發(fā)現(xiàn)和理解建筑的元素，網(wǎng)格、框架、柱、梁、板、中心、外圍、場域、邊緣、線、面、體、擴(kuò)展、壓縮、緊張、剪切等。學(xué)生們開始探索平面、立面、剖面以及細(xì)部節(jié)點(diǎn)的意義。他們學(xué)會了如何繪制。他們開始理解二維圖紙，軸測投影及三維（模型）之間的關(guān)系。學(xué)生們在平面和軸測圖上研究和繪制自己的方案，并通過模型探究其三維結(jié)果。于是，對要素的理解開始明晰，建構(gòu)的理念開始涌現(xiàn)。

九宮格問題

按1/4英寸=1.0英尺的比例建立如下模型。用鉛筆在描圖紙上按下圖繪制30/60度等軸測。這個(gè)模型和圖紙將作為研究和學(xué)習(xí)九宮格問題的基本操作工具。

柱-白色，底板-黑色，隔板-灰色。一個(gè)15英尺網(wǎng)格分成5等份和3等份，一個(gè)16英尺網(wǎng)格分成1等份和2等份。

九個(gè)方格介于完全自由流動與完全獨(dú)立封閉的兩極之間。

中心與外圍的概念。一個(gè)中心網(wǎng)格，八個(gè)外圍網(wǎng)格。

取完整的隔墻（模型），在9個(gè)方格（16根柱）中研究空間關(guān)系。然后將方案用鉛筆在軸測圖中繪制。這種形式研究可以通過以下問題進(jìn)行下去。

1. 完整隔板（墻）。

2. 1/2隔墻（水平向/縱向）。

3. 完整隔墻和1/2隔墻組合。

4. 曲墻與半圓隔墻組合。

5. 完整隔墻與曲墻組合。

6. 隔墻，半墻與曲墻組合。

7. 完整隔墻轉(zhuǎn)45°或60°，或45°與60°隔墻組合。

8. 完整隔墻與45°或60°隔墻組合。

9. 完整隔墻（90°，60°，45°）的1/2與曲墻組合。

10. 將以上系統(tǒng)脫離柱網(wǎng)框架（不觸及那些柱子）。

11. 放置一系列體量（圓形、方形或三角形），三角形、正方形體量底邊或圓形直徑)從1英尺到10英尺不等，高度也從1英尺到10英尺不等。

12. 將柱與隔墻板以一系列不同的組合方式聯(lián)結(jié)。

13. 創(chuàng)建樓梯，坡道，直跑樓梯，U形樓梯，圓形樓梯，直跑坡道，U形坡道。

14. 創(chuàng)建第二層框架并延續(xù)之前的研究。

15. 創(chuàng)建第三層框架并延續(xù)之前的研究。

16. 建立1/2圓，1/2菱形，1/2方形屋頂結(jié)構(gòu)。

17. 聯(lián)結(jié)以上系統(tǒng)。

1. 本篇英文原稿及插圖除特別注明外均來自于Mask of Medusa，by John Hejduk；

2. ?”=1’–0，比例尺表示方法，即?”=1’0”，?英寸=1英尺的比例。

3. panel, a section or division of a wall, ceiling, or other surface. 因此這里翻作隔墻。