Gaudi 작품속에 기하

마방진

Jesus and Judas with the Magic Square.

 

 가로, 세로, 대각선의 합이 33(= 죽을 때 여수의 나이)

 10×2 + 14×2 = 48

 The number 48 is the same number one obtains

 if the letter of INRI (Iesus Nazarenus Rex Iudeourum) are assigned a number according to their order in the Latin Alphabet.

A	B	C	D	E	F	G	H	I	K	L	M	N	O	P	Q	R	S	T	V	X
1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21

 

So that 9 + 13 + 17 + 9 = 48

 

Tesselations

 

타일을 깨 붙여서 곡면을 표현하는 trencadís 기법

 

DOUBLE TWISTED COLUMN

 

 

 

Catenary Arches and Catenoids

hyperbolic cosine 함수

 

 

줄의 양끝을 고정시켜 늘어지게 했을 때 생기는 곡선이 현수선

가벼운 소재로 만들어도 큰 무게를 지탱할 수 있는 강점이 있다. 

늘어진 체인이 catenoid를 형성

아치건물의 외부에 반영

현수선에 추를 달아서 무게가 있는 모델

스페인 Santa Coloma de Cervello 에 있는 교회의 디자인

Conic Sections

 

Parabolas(포물선) 2차곡선

원추곡선 포물선, Palau Guell 의 포물선 출입문, Palau Guell 의 다락방

 

Hyperbolas(쌍곡선) 

double cone 의 단면, 쌍곡선이 보이는 단면도, Sagrada Familia 의 천정

 쌍곡선은 깊고 먼 느낌을 준다.

 

Ruled Surfaces

 

Hyperboloids of one Sheet

실린더를 살짝 비틀어서 만든 hyperboloid

Model of Hyperboloid,      Sagrada Familia 의 회랑벽

 

Hyperbolic Paraboloids

the Sagrada Familia의 박물관 hyperbolic paraboloid 모델, 

마치 말안장을 연상시키는 컴퓨터로 만든 모델, 

Arch by Gaudi

Sagrada Familia성당 돔지붕의 내부와 외부에서 본 인테리어

 

 

여러 곡선과 곡면

 

기둥에 circular helix

A side view of the school, showing the sine wave like cross section of the roof. Image:Aidan McRae Thomson

A ruled surface from the Museum in the Sagrada Familia

Sagrada Familia성당에 Helicoidal 계단

Ellipsoid

 

The main contributions Gaudí made to architecture that can be seen in the Sagrada Familia are:

Hyperboloids

  Watch vid

They can be solid as in the junctions between the columns and the vaulting, or hollow to allow light,

symbol of God for Gaudí, to enter the temple. They can be found in the openings of the windows and the vaults.

Paraboloids

Gaudí used paraboloids to create linking surfaces between the vaults and the roofing and the columns on the Passion facade,

as well as larger elements such as the towers and the sacristies. For him they represented the Holy Trinity.

Helicoids

According to the iconography of Gaudí they represent the rising movement that links the earth wi heaven.

Here they can be seen in the spiral staircases.

Ellipsoids

Gaudí generated the rounded capitals of the main columns from ellipsoids,

where the lower columns subdivide into branches.

Double-twisted columns

To achieve greater stability and a slender and more harmonious effect,

Gaudí designed all the branching columns as double-twisted columns formed by two helicoidal columns.

The base of each column has a cross-section that is a polygon or star which as it twists to the right and the left transforms into a circle higher up.