TRIANGLE

6:13:00 PM

I felt Triangle meant a lot to me & I do a research about it. It is useful to know more about a shape in Design-based students or Designers. People would be questioning why do I interested in Triangle only instead of other geometry shapes? No, there is no reason because I love the word TRIANGLE.


*image taken from bigbackground,com*


Before starting the lesson, I found a lot things & website that makes me feel curious, about Geometry.

There is an Academy starting a high-school level course on Geometry (which is based on Euclid's elements) in Math category. "It revisits many of the basic geometrical concepts studied in earlier courses, but addresses them with more mathematical rigor." They said.

The Euclidean Geometry was to started roughly 2400 years ago. Euclid of Alexandria which nobody know the exact date he born, around mid 4th century BCE and died around mid-3rd century BCE. He was featured in Raphael's School of Athens. (sounds like in some game places), he was a Greek Mathematician & called as "Father of Geometry". He is the one who wrote Elements serving as the main textbook for teaching mathematics. Euclid deduced the principles of what they called Euclidean Geometry from a small set of Axioms. Euclid in Greek name meaning "Good Glory". To know how does he look like, refer to picture below.

*image taken from 1st-art-gallery.com*

In the course will be learning further information about Angles & intersecting lines, Congruence, Similarity, Right triangles & trigonometry, Perimeter, Area & Volume, Circles, Special properties & parts of triangles, Quadrilaterals, Transformations, Analytic Geometry, Geometry constructions & more than 80 problems Worked examples.

This academy called Khan Academy, from www.khanacademy.org. (Info found under Math's category.)

Then, on the way of searching the histories and information, I found a movie called TRIANGLE.
Date released: 16 October 2009 (UK)
Type of movie: Mystery, Thriller
Director & Writer: Christopher Smith
Stars: Melissa George, Joshua McIvor, Jack Taylor & more.




Let's start with the Geometry.

1. How did the Geometry shape was formed?
From my knowledge of my history subjects, the earliest geometry is from Mesopotamia and Egypt in the 2nd millennium BC. the earliest known texts on geometry are the Egyptian Rhind Papyrus (2000-1800 BC) and Moscow Papyrus (c.1890 BC). In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems and he is credited with the use of deductive reasoning applied to geometry. Around 300 BC, it revolutionized by Euclid. As what I mention above, Euclid Alexandria. [GEO "Earth"]. As everyone know, Geometry is concerned about shapes, size, relative, position of figures and the properties of space. A mathematician who works with Geometry called Geometer. Geometry is concerning lengths, areas & volumes, with elements of formal mathematical science.

In Euclid's time, there was no clear distinction between physical and geometrical space. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space which they only approximately resemble at small scales.

Geometry originated as a practical science concerned with surveys, measurements, areas and volumes. Among the other highlights, notable accomplishments include formulas for lengths, areas and volumes, such as the Pythagorean theorem, circumference and area of a circle, area of a triangle, volume of cylinder, sphere, pyramid. This is all what we are learning during the secondary school or high school in the Mathematics textbook.

Classically, the only instruments allowed in Geometric constructions are Compass & Straightedge. And now, we don't need instruments to do so if we know the computer software like Autocad (example).

File:Geometry Lessons.jpg
*image taken from wikipedia*

This was during the Geometry lessons in the 20th century.


And, this is now using the computer software, Autocad to do it. Simple and fast.

In nearly 2000 years ago, Eucildean geometry was synthetic a priori that overturned by the non-Euclidean geometry in the words of Bolyai, Lobachevsky Gauss who never published his theory. 

In the middle ages, mathematics in medieval Islam contributed to the development of geometry, especially the Algebraic geometry and Geometric Algebra. Thabit ibn Qurra (known as Thebit in Latin) dealt with arithmetric operations applied to ratios of geometrical quantities and contributed to the development of Analytic geometry. 

Alright, that's all I could re-synopsis it about Geometry, It was a long long history about it and you should go Wikipedia or google search about it or even buy a book to read the history! I don't continue it because there will make my whole topic gone! Topic today was Triangle nor Geometry. Geometry is just a start of it to introduce about the shapes and how it formed. 

2. What is Triangle? (If people ask you to explain)
A really good question, if the kids ask you what is triangle? Why triangle to be this shape? Why and why again. 

Triangle is a basic geometric shape which come together with Circle, Square and Rectangle. Rectangle shouldn't be in basic geometric because it's under square category but never mind, put it in. It's a polygon with three corners or vertices and three sides or edges which are line segments. 


Triangles can be classified according to the relative lengths of their sides:
- In an Equilateral Triangle. All sides to be same length and with all angles measuring 60°.
- In an Isoceles Triangle. Two sides are Equal in length and angles.
- Scalene Triangle. It is a triangle with no equal sides and no equal angles, as long as 3 sides, 3 vertices.


             Equilateral Triangle                              Isosceles triangle          Scalene triangle

Internal Angles:
- Right-Angled-Triangle (formerly called Rectangled Triangle) with internal angles 90. The side opposite to the right angle is called Hypotenuse, it is the longest side of the right triangle. Two sides called Legs of Catheti. The sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2 where a and b are the lengths of the legs and c is the length of hypotenuse. 

- Oblique Triangles that do not have an angle that measures 90°.

- Acute Triangle / Acute-Angled triangle has all interior angles less than 90°

- Obtuse triangle / Obtuse-Angled triangle has more than 90. 


There is some basic facts of Triangles that are assumed to be two-dimensional plane figures. A triangle showing exterior angle D. An exterior angle of a triangle is an angle that is a linear pair to an interior angle.


Stop the history and I know nobody will read it, as it is boring and you will think what is it for to know? Duh.

Here's a little flash back time for my high school mathematics class.

To calculate perimeter is very easy, you just need to take all the distance around the edge of the triangle and sum up then the answer appear. For area, I think in primary we learn about it? I'm not sure. Its actually a formula that we always remember: Area = 1/2 x Length x Height (length is the horizontal side of the triangle). But usually people always use B as the length : 1/2 x b x h & another way is bh/2.

And I got something, I know it last time when I was in secondary school. But I always think that its fun.

*image from mathisfun.com*

Nah, I know everyone knows it, but maybe I'm the kiddo that always think it is so curiousness. A doubled triangle will be forming a square by the formula. Kinda stupid, I know what you all thinking about.

There is actually more formulas to go to the higher level that I should know. I have studied about it while research. But I'm kind of lazy to summarize it with a long long sum formula. Nah, the website to see, scroll down to the bottom and you will study the further studies of the formulas. HERE

Uh Uh ~ No, not finished yet! I haven't talk about the Building Construction of Triangles. Hahaha, my lecture is so boring and so long. "Hey students, sit still and listen!" lol.

3. Building Constructions of Triangle.
Normally or Usually, the older days, people build more Rectangular buildings and it is most popular and common geometric form for buildings. Am I right? Because it is so easy to construction with 4 corners and 4 sides with simple dimensions and measurement is so easy to get. But have you think how to measure an accurate angle during the construction? Haha, there is a machine or ways to do it la, I don't know yet. I want to tell is Triangle building is much more difficult to use conceptually or provide a great deal of strength. Is it stable? People would be asking before constructing, but also depending on the height of the building. Of cause, short will be much more stable. But how is its a commercial tall building?

As computer technology helps the Architects design creative new buildings and Triangular shapes are becoming increasingly prevalent as the primary shape of some types of skyscrapers as well as the building material they used. Nah, I found an history about Tokyo in 1989, Achitects had wondered whether it was possible to build a 500-storey tower to provide affordable office space for this densely packed city. But! with the danger of earthquakes, Architects considered that a triangular shape would have been necessary so then it hasn't by 2011.

In New York City, the blocks cut like triangles and buildings have been built on these shapes! The Flatiron Building in New York is shaped like a triangular prism. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs in New York.



Triangles are sturdy; while a rectangle can collapse into parallelogram from pressure to one of its points. triangles have a natural strength which supports structures against lateral pressures. Did you WOW? Also, a triangle will not change shape unless its sides are bent or extended or broken or its joints break! Sounds like "hmm...." In essence, each of the 3 sides of triangle supports the other 2.

From now, people are not building triangle buildings as in the floor plan is triangle to the top. I cant really find pictures of building of it. But most designers use triangle elements in the building such as The Disney Epcot Center dome, Sir Norman Foster's Hearst Building on Eighth Avenue at 57th St. and more........

Transamerica Pyramid is the tallest skyscraper in the San Francisco skyline. It is triangular shaped tall building consists of 48 floors and 853 ft (260m) of a structural height. Construction began in 1969 and finished in 1972 but the building no longer houses the headquarters of the Transamerica Corporation and move their U.S. headquarters to Baltimore, Maryland. Designed by architect Willian Perira and built by Hathaway Dinwiddie Construction Company. This considered 8th tallest building in the world.

TransAmBldg 3871.jpg


Image from buzzbuzzhome.com

Eiffel Tower, it's actually not consider a triangular in plan because it has 4 legs or unless it deconstruct into 3 legs. Haha!! As everyone know, it famous and a landmark in Champ de Mars, Paris. In french called "La Tour Eiffel". It was named after the engineer Gustave Eiffel whose company designed and built the tower from 1889 as the Entrance arch to the 1889 World's Fair. It has become both global cultural icon of France and one of the most recognizable structures in the world. Yeah, everyone know YOU! Also known as the tallest structure in Paric and most visited paid monument, 6.98 million people ascended it in 2011!!!! WOW! The tower is 324 metres tall (1,063 ft) about a height as an 81-storey building. 

The tower was built with the puddled iron as wrought iron structure of the tower weighs 7,300 tonnes with its non-metal components is approximately 10,000 tonnes. It is a wind considerations tower. Eiffel used empirical and graphical methods accounting for the effects of win rather than a specific mathematical formula. 


And now, many people designed own Eiffel tower, imagine it is so popular and it's lady's lover! I also wish to go to Paris for my Honeymoon, its one of my honeymoon vacations, not only one! Haha.

To know more, http://www.tour-eiffel.fr/ - The official website of Eiffel Tower, NOW!

Wellness Sky by 4of7, the building named 'Danube Flower' was built some 35 years ago to become a landmark of Belgrade waterfront.


floor plan

*more image & information from http://www.archdaily.com/11153/wellness-sky-4of7/*

Now, is the end of the topic, will be ending with lotsa Triangular Buildings or Triangular elements buildings.


La Projet Triangle by Herzog & de Meuron


Shading System


Royal Ontario Museum in Toronto


Federation Square, Melbourne


Sparkling Hill Resort Vernon, British Columbia (Cannon Design)

Fuksas-Myzeil – shopping mall, part of the "PalaisQuartier"
Fuksas-Myzeil – shopping mall, part of the "PalaisQuartier"
Fuksas-Myzeil – shopping mall, part of the "PalaisQuartier"

Myzeil Shopping Mall
http://www.architonic.com/aisht/myzeil-shopping-mall-part-of-the-palaisquartier-fuksas/5100026


New Year's eve ball, atop One Times Square, New York City.


Quilt from http://www.diaryofaquilter.com/


And even the DIY stuff, Modular Origami 


Research Duration: 1 whole day
Image from: GoogleKeyword: Triangle
Resources:
- Wikipedia
- Google
- WyzAnt
- Math is fun
-Rogers Connection
- Architonic
- Citylab
- RadioActiwe, Tumblr
- Dezeen
- Some oversea bloggers
Research done by: Isabellxiaolin




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