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6.5 Ingenious Calculations by Folk Carpenters课程教案、知识点、字幕

五 民间木匠的巧妙计算

木质的圆桶 圆盆

是民间工艺中的一种立体造型

对它的设计是民间木匠不可缺少的工序

在农村的圆形木桶和木盆制造中

民间的木匠要解决一个既复杂又简单的问题

就是计算圆桶“瓦子”的夹角

这是一个木制圆桶的立体示意图

和一张横截面图

在木桶的制作中

这个木桶是由N块“瓦子”组成的

什么叫“瓦子”

就是构成木桶的一块一块的木板

因为这个木板有点弯曲 像瓦的形态

所以叫“瓦子”

这多块“瓦子”构成了一个木桶

每块“瓦子”的夹角应该是多少呢

我们找了两块木板 这个“瓦子”

就像这一块块的木板 这样围起来

这个木板之间必须有个夹角

做起来才不会漏水

带着这个问题我请教了几位数学博士

他们虽然给出了

每块“瓦子”夹角的计算公式

但是却算不出每块“瓦子”的夹角是多少度

为什么

因为每块“瓦子”的宽窄因木料大小的不同

它是一个变量

没有人能预先知道我做这个木桶

要用到多少块“瓦子”

还有每块“瓦子”的宽窄 就是弧长

也是一个不定的数

这样 数学博士给我的这个公式就没法计算

这个公式就是

θ 等于360乘上L 就是弧长

再除以2πR

但是

民间木匠利用一种叫做“规尺”的工具

他可以在短短的几秒钟时间内

迅速准确地算出每块“瓦子”的夹角

并把它制作出来

这把“规尺”

就是我托人从我43年前学木匠的地方

湘西土家族苗族自治州永顺县梁庭坳弄塔村

从一个王姓的木匠那里找来的

下面我们来分析一下“规尺”的工作原理

1 我们看 “规尺”上面有很多圆孔

它是每隔半寸钻一个孔

这是为了匹配圆形木桶的半径

而设置的半径的轴心

2 “规尺”以轴心为基点

可以作大小的张开角度

以迎合宽窄不同的“瓦子”

比如说 这是一块木板

这个夹角应该是多少呢

他用这个(规尺) 一靠 一掐

这条木板夹角的这条边

跟“规尺”的这个边如果重合之后

正好就是需要的夹角

如果不重合 就把这块木板刨一刨

加工成跟它完全一样的角度

这样做起来就不会漏水

民间木匠虽然不认识几个字

有的甚至是文盲

他们在这里采用了“动态测量”的方法

解决了高等数学都无法解决的

看似简单 实为复杂的计算

体现了中国木匠巧妙的思维和高超的智慧

民间图形中还蕴含了许多中国智慧的闪光点

我们这节课不可能面面俱到

通过中国智慧的学习

可以激发我们对中国优秀传统文化的热爱

启发我们的创造性思维

这一节就讲到这里

谢谢大家

Chinese Folk Motif Arts课程列表:

Unit 1. Folk Motifs: Basic Categories and Characteristics

-A brief introduction of the study unit

-1.1 The meaning of learning Chinese folk motifs

--1.1 The meaning of learning Chinese folk motifs

-1.2 A brief introduction of graph

--1.2 A brief introduction of graph

-1.3 The basic categories of Chinese folk motifs

--1.3 The basic categories of Chinese folk motifs

-1.4 The basic characteristics of Chinese folk motifs art

--1.4 The basic characteristics of Chinese folk motifs art

-1.5 Research on the questions and the motifs cases

--(1) Researches and case studies on motifs

--(2)Research on Traditional Motifs

-1.6 Unit assignment: thinking questions

--Question 1

--Question 2

-1.7 Online Quiz

--1.7 Online Quiz

-1.8 Expanded learning resources

--Embroidery of Guizhou Miao ethnic group (Video)

--The Magnificent Miao Ethnic Group: Wordless Book of Miao (Video)

--Chinese Folk Motifs(Graphics and images)

--Monographs

--Websites

--Reference Papers

Unit 2. Motif Arts : Modeling Methods and Aesthetic Significance

-A brief introduction of the study unit

-2.1 The modeling methods of folk motifs

--2.1 The modeling methods of folk motifs (Part 1)

--2.1 The modeling methods of folk motifs (Part 2)

-2.2 Aesthetic implication of folk motifs

--2.1 Aesthetic implication of folk motifs (Part 1)

--2.2 Aesthetic implication of folk motifs (Part 2)

-2.3 Research on the questions and the motifs cases

--Graphics cases 1

--Motifs cases 2

--Research on the questions

-2.4 Art Practice: Canton Embroidery

--Meet Canton Embroidery 1

--Meet Canton Embroidery 2

--Meet Canton Embroidery 3

-2.5 Unit assignment: Judgment and thinking questions

--Judgment questions

--Thinking question 1

--Thinking question 2

-2.6 Expanded learning resources

--My hereditary treasure: new year woodblock print made by Tai Liping (Video)

--Taohuawu new year woodblock print (Graphics)

--Monographs

--Reference Papers

Unit 3. Chinese Shadow Puppetry: Characters Developed by Scissors and Nicking Chisels

-A brief introduction of the study unit

-3.1 A Brief Introduction of Chinese Folk Paper Cut

--3.1 A Brief Introduction of Chinese Folk Paper Cut

-3.2 The craft of Chinese folk paper cut

--3.2 The craft of Chinese folk paper cut

-3.3 The techniques of expression of Chinese folk paper cut

--3.3 The techniques of expression of Chinese folk paper cut

-3.4 A brief introduction of Chinese shadow puppetry

--3.4 A brief introduction of Chinese shadow puppetry

-3.5 The artistic characteristics of Chinese shadow puppetry

--3.5 The artistic characteristics of Chinese shadow puppetry

-3.6 The modeling of Chinese shadow puppetry

--3.6 The modeling of Chinese shadow puppetry

-3.7 Art Practice: Paper Cut

--A Brief Introduction of Art Practice

--Traditional Chinese Paper Cutting : Butterfly

--Traditional Chinese Paper Cutting : Baby with twisted knors of har

--Paper-cut creative case (picture)

-3.8 Unit assignment: Paper Cut creation

--Paper Cut creation

--Question 1

--Question 2

-3.9 Online Quiz

--3.9 Online Quiz

-3.10 Expanded learning resources

--Paper-cut works (picture)

--Backstage performance of shadow play (video) (Ⅰ)

--Backstage performance of shadow play (video) (Ⅱ)

--Shadow play "Monkey Eating Peach"

--Analysis of Chinese Shadow Puppet Art

--Reference Papers

Unit 4. The Heritage of Chu Culture: Discovering the Intangible Cultural Heritage

-A brief introduction of the study unit

-4.1 The State of Chu and Chu Culture

--4.1 The State of Chu and Chu Culture

-4.2 Representative Graphics of Chu Culture Remains

--4.2 Representative Graphics of Chu Culture Remains

-4.3 Intangible Cultural Heritage of Chu Culture

--4.3 Intangible Cultural Heritage of Chu Culture (Part 1)

--4.3 Intangible Cultural Heritage of Chu Culture (Part 2)

-4.4 Research on the questions and the motifs cases

--Chu Culture Relics Graphics

--The motifs case : Tujia ethnic Brocade "Xilan Kapu"

-4.5 Art Practice: Decorative painting

--Art Practice: Decorative painting sketch

--Art Practice: Decorative painting modeling

--Art Practice: Decorative painting coloring

-4.6 Unit assignment

--4.6 Unit assignment

-4.7 Online Quiz

--4.7 Online Quiz

-4.8 Expanded learning resources

--Bronze ware, lacquerware, silk fabrics of Chu culture

--Yao ethnic bright-colored embroidery applique, Dong ethnic brocade

--Monographs

--Reference Papers

Unit 5. The Final Totem: The Mysteries Behind Folk Motifs of Various Ethnic Groups in China

-A brief introduction of the study unit

-5.1 Totem

--5.1 Totem (Part 1)

--5.1 Totem (Part 2)

-5.2 Panhu Worship

--5.2 Panhu Worship

-5.3 The Legends of Totem in Costumes

--5.3 The Legends of Totem in Costumes

-5.4 The Tattoos of the Li Ethnic Group

--5.4 The Tattoos of the Li Ethnic Group

-5.5 Art Practice: Tie-dye

--Introduction of Tie-dye

--Xiang Yunfang tie-dyeing (clamp-tie) video

--Xiang Yunfang tie-dyeing (bundle-tie) video

--Xiang Yunfang tie-dyeing (dog-paw flower) video

-5.6 Research on the questions and the motifs cases

--Totem problem exploration

--Traditional graphics cases:The "Hundred-bird Clothes" of the Miao ethnic in Guizhou

-5.7 Unit assignment: Tie-dye creation and thinking questions

--5.7 Unit assignment: Tie-dye creation and thinking questions

-5. 8 Expanded learning resources

--Miao embroidery in Taijiang (Video)

--The Magnificent Miao Ethnic: Who made life so glorious (Video)

--National costumes of southern China

--Guizhou Miao ethnic paper-cutting, Shui ethnic horsetail embroidery, Miao ethnic batik, Miao ethnic Embroidery

--Monographs

--Reference Papers

Unit 6. Chinese Folk Motifs and Chinese Wisdom

-A brief introduction of the study unit

-6.1 Philosophical Reflections on the Harmony of Taiji and “Yin and Yang”

--6.1 Philosophical Reflections on the Harmony of Taiji and “Yin and Yang”

-6.2 “Nine Palaces” and Its Spatial Layout

--6.2 “Nine Palaces” and Its Spatial Layout

-6.3 Plane Static Four-dimensional Space

--6.3 Plane Static Four-dimensional Space

-6.4 “Almorphism” of Batik Graphics

--6.4 “Almorphism” of Batik Graphics

-6.5 Ingenious Calculations by Folk Carpenters

--6.5 Ingenious Calculations by Folk Carpenters

-6.6 Research on the questions and the motifs cases

--Research on the questions and the motifs cases

--Introduction to Miao Batik (Video)

--Danzhai Batik - Painting Wax (Video)

-6.7 Unit assignment: thinking questions

--6.7 Unit assignment: thinking questions

-6.8 Online Quiz

--6.8 Online Quiz

-6.9 Expanded learning resources

--The image of dragon in Chinese folk motifs (graphic and image)

--Monographs

--Reference Papers

6.5 Ingenious Calculations by Folk Carpenters笔记与讨论

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