geometry and creativity

MK. METODOLOGI DESAIN

GEOMETRI

GEOMETRI MATEMATIKA

1. A group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

2. A mathematical operations and processes involved in the solution of a problem or study of some scientific field

1. Ilmu yang mempelajari tentang besaran, struktur, bangun ruang, dan perubahan-perubahan yang pada suatu bilangan.

2. Ilmu tentang bilangan dan segala sesuatu yang berhubungan Pengertian matematika dengannya yang mencangkup segala bentuk prosedur operasional yang digunakan dalam menyelesaikan masalah mengenai bilangan.

The area of mathematics that deals with points, lines, shapes and space.

Salah satu cabang matematika yang bersangkutan dengan perihal bentuk, ukuran,

posisi relatif tokoh, dan sifat ruang.

Garis dan bidang dapat dideskripsikan dengan dua cara, yaitu melalui cara matematik dan melalui bentuk geometrik.

Melalui cara matematik, bentuk, garis dan bidang terbentuk melalui sistem koordinat, sehingga untuk membuat bentuk tertentu, diperlukan rumus-rumus dan hasil yang 100% tepat.

Bentuk, garis dan bidang juga dapat terwujud tanpa melalui rumus-rumus eksak matematika, yaitu dengan menggunakan instrumen-instrumen geometri yang sudah ada. Sehingga tidak memerlukan hitungan yang 100% tepat untuk mengetahui bentukan bola atau lingkaran. Begitu juga dengan kubus, balok dan persegi panjang.

Functions of Geometry

Menyusun bentukan-bentukan geometris dengan mudah.

Mendeskripsikan bentuk secara tepat.

Semua orang bisa menikmati bentuk-bentuk geometris yang mutlak dan sempurna.

Memberi kita bentuk-bentuk yang siap untuk digunakan dan bisa diolah sedemikian rupa dengan bermacam-macam cara.

The Appeal of Geometry

1) Menghasilkan palet lahirnya berbagai bentuk yang tidak dapat disangkal secara rasional bagi arsitek (menjadi bukti/alasan formal adanya bentuk-bentuk lain).

2) Membuat arsitek merasa nyaman dengan penggunaan bentuk yang bisa diperbanyak dan diulang jika diperlukan tanpa rasa takut akan membuat kesalahan.

3) Menawarkan kebebasan luar biasa dan tanpa paksaan untuk keluar dari bentuk-bentuk yang sudah di-pakem-kan di masa lalu (seperti bujur sangkar yang mendapat interpretasi proporsional yang tidak terbatas; maka akan demikian halnya dengan bentuk-bentuk lain).

4) Menawarkan disiplin baru mengenai pandangan dunia luas. Dulu, ketika diperkenalkan kepada arsitek, diibaratkan ada kemungkinan untuk mencapai Tuhan dan mencapai suatu keagungan jika mereka menggunakan bentuk-bentuk umum seperti bujur sangkar, lingkaran dan segitiga.

5) Menawarkan jaminan psikologis, dimana geometri memungkinkan variasi pengaruh psikologis manusia (perasaan berbeda) yang muncul ketika ada perbedaan proporsi pada suatu bentuk.

6) Memberikan komunikasi yang kuat kepada masyarakat akan keikutsertaan arsitek melalui pengetahuan geometri dan itu berarti ada identifikasi secara sosial dan jasa arsitek diakui secara profesional.

7) Memberi lebih banyak waktu untuk berpikir, mengeksplor, memanipulasi dan menggunakan bentuk-bentuk dasar secara maksimal daripada menghabiskan waktu mereka untuk menemukan bentuk baru setiap harinya.

Types of Geometry

Bentuk geometri terdiri dari tiga jenis, yaitu bentuk geometri yang telah terdefinisikan (divine, undeniable), bentuk geometri bebas (free form), dan combinasi keduanya (combinatorial form)

Bentuk geometri bebas adalah bentuk-bentuk yang dibuat secara bebas, bisa dengan mengutak-atik bentuk yang sudah ada atau bisa juga dengan membuat bentukan baru yang belum terdefinisikan sebelumnya.

Free Form

Karakteristik bentuk bebas (free form)1. Tidak bisa diprediksi

(unpredictable)2. Sulit untuk pembenaran (difficult to

justify)3. Sulit digambar (difficult to draw) dan

sulit dibangun (difficult to construct)4. Bersifat Individualistic

Free Form

Tipe-tipe bangunan yang pernah menggunakan pendekatan geometri:1. Monofunctional buildings2. Complex building types3. Literal combinations of free and

divine (monofunctional or multifunctional)

4. The arbitrary combinations

Megaron

Shezade Mosque

The Einstein Tower Hobbit Astrophysical Observatory in Germany

House IV Peter Eisenman

Sumber : http://flavorwire.com/330293/10-amazing-examples-of-architecture-inspired-by-mathematics

Mobius Strip TempleA similar twisty shape is applied to the design of Buddhist buildings. The temple is a mound-like shape known as a stupa similar to a pagoda and contains a central spire where Buddhists congregate. One architect wanted to modernize it for a soon-to-be built temple in China, and based the updated design on the Mobius Strip which also happens to symbolize reincarnation.


Tetrahedral-Shaped Church

The tetrahedron is a convex polyhedron with four triangular faces. Youve seen the same geometric principle used in RPGs, because the dice is shaped the same. Famed architect Walter Netschapplied the concept to the United States Air Force Academys Cadet Chapel in Colorado Springs, Colorado. Its a striking and classic example of modernist architecture, with its row of 17 spires and massive tetrahedron frame that stretches more than 150 feet into the sky.


Pentagonal, PhyllotacticGreenhouse and Education Center

Cornwall, Englands Eden Project is home to the worlds largest greenhouse, composed of geodesic domes that are made up of hexagonal and pentagonal cells. Their interactive education center dubbed The Core incorporated Fibonacci numbers (a math sequence that also relates to the branching, flowering, or arrangement of things in nature) and phyllotaxis (the arrangement of leaves) in its design.


A Mathematically-Inclined Cucumber in the Sky

Standing 591-feet tall, with 41 floors is Londons skyscraper known as The Gherkin. The modern tower was carefully constructed with the help of parametric modeling amongst other math-savvy formulas so the architects could predict how to minimize whirlwinds around its base. The designs tapered top and bulging center maximize ventilation. The building uses half the energy of other towers the same size.


Experimental Math-Music Pavilion

Philips Electronics Company wanted to create the experimental space, calling it the first electronic-spatial environment to combine architecture, film, light and music to a total experience made to functions in time and space. It was through these visually inspired concepts that elevated the Philips Pavilion into a complete experience where one could visualize their special movements through a space of sound, light, and time.


Modern Music-Math Home

The curved, elegant structure which also serves as an incredible concert space for 200 people was named the Integral House. The homes owner Jim Stewart was a calculus professor who wrote textbooks and wanted to incorporate the mathematical sign into the homes name and design. Undulating glass and wood walls also echo the shape of a violin.


Solar Algorithm WizardryBarcelonas Endesa Pavillion used mathematical algorithms to alter the cubic buildings geometry, based on solar inclination and the structures proposed orientation. Algorithms can be used to create the perfect building for any location with the right computer program. For Endesa, the movement of the sun was tracked on site before an architect from the Institute for Advance Architecture of Catalonia stepped in to complete the picture.


Cube Village

Cube Village, built by Dutch architect Piet Blom. His tilted, geometric houses built on top of a pedestrian bridge to mimic an abstract forest are split into three levels. The top has windows on every facade and feels like a separate structure entirely.


Magic Square Cathedral

The Sagrada Familia cathedral in Barcelona designed by Antoni Gaud is a mathematicians dream. Hyperbolic paraboloid structures are featured throughout. Catenary arches (a geometric curve) abound. The cathedral also contains a Magic Square an arrangement of numbers that equal the same amount in every column, row, and diagonal.


Fractal Gas Station Makeover

A fractal is a fragmented geometric shape that is split into several parts, but each of those components is just a smaller-sized copy of the overall form. Many architects apply this mathematical principle to their building designs that recently had a green makeover. Everything has been stripped down including the filling stations signs, which are subtle symbols and the mirrored facade beautifies ninety solar panels that power the station. Recycled materials and a plant-covered roof complete the enviro-friendly revamp.

geometry and creativity

Documents