The special property of the Golden Rectangle is that the ratio of its length to its width equals approximately 1.618: 2 Golden Ratio = ______ Length Width ≈ 1.6 3 The Golden Rectangle
Trang 11 The Golden Rectangle is a very important shape in mathematics The Golden Rectangle appears in nature and music It also is often used in art and architecture The special
property of the Golden Rectangle is that the ratio of its length to its width equals approximately 1.618:
2 Golden Ratio = Length Width ≈ 1.6
3 The Golden Rectangle is considered to be one of the most pleasing and beautiful shapes to look at That is why many artists have used it in their work Leonardo da Vinci and Piet Mondrian are perhaps the most famous for using the golden ratio
property characteristic of something ratio relationships between two numbers approximately close, but not exact
The Golden Rectangle
Analyze Author’s
Viewpoint What
words used by the
author are clues to
his viewpoint on the
Golden Rectangle?
Do you agree?
Reading
Strategy
Content
Mathematics
Reading 2
By using one golden rectangle to create another (above), you create the pattern
of a spiral, which is found in nature in the Nautilus shell (right).
Trang 24 Leonardo da Vinci
5 Leonardo da Vinci was a great Italian Renaissance
painter He was also a scientist and inventor In his art, da
Vinci carefully examined the proportions of the human
body He found many occurrences of the golden ratio and
golden rectangles
6 Art Masterpiece: Mona Lisa
7 You have probably heard of the Mona Lisa The Mona Lisa
is one of the most famous paintings in the world It is a very
good example of da Vinci’s use of the golden ratio in art
8 If you draw a rectangle around Mona Lisa’s face, that
rectangle will turn out to be “golden.” The dimensions of
the painting itself also form a golden rectangle As well, the
proportions of Mona Lisa’s body exhibit several golden
ratios For example, a golden rectangle can be drawn from
her neck to just above the hands
Renaissance time period beginning in the 1500s in Europe when classical art
was popular
examined looked at closely
occurrences how many times something happens
exhibit show
Analyze Author’s Viewpoint
Do you think the author admires
da Vinci? Support your answer with examples from the text
Reading Strategy
Reading Check ✓
1 Recall facts
What is a special property of the golden rectangle?
2 Identify proposition/
support Identify
the idea in paragraph 1 that the author proposes and the support that the author provides
3 Make an inference
Do you think da Vinci used the golden rectangle
in other paintings
or only in the Mona
Lisa?
Trang 39 Piet Mondrian
10 Piet Mondrian is a modern
Dutch artist, who lived 1872 to 1944
Although he painted many landscapes
at the beginning of his career,
Mondrian later moved to an abstract
style in his work
11 Mondrian is famous for using
horizontal and vertical black lines
as the basis for a lot of his paintings
Like da Vinci, Mondrian believed that mathematics and art were closely connected He used the simplest geometric shapes and primary colors
(blue, red, yellow) to express reality, nature and logic from a
different point of view
12 Mondrian’s point of view is that any shape can be created with basic geometric shapes His point of view is also that
any color can be created with different combinations of red,
blue, and yellow The Golden Rectangle is one of the basic shapes that keeps appearing in Mondrian’s art:
14 • Take a blank piece of paper
• Prepare different colored pencils
• On a separate sheet of paper, practice drawing golden
rectangles of different sizes and colors
• Plan out your original design How are you going to
arrange the rectangles on paper?
• Draw your design Experiment with the different colors
and sizes of your golden rectangles (You can also draw some rectangles that aren’t golden See how those rectangles change the effect.)
• Frame your work and decorate your wall.
modern belonging to the period of abstract art from the late 19th century
to the mid 20th century
abstract not representing anything real horizontal parallel to the ground vertical pointing between the ground and the sky logic a way of reasoning
Analyze Author’s
Viewpoint Do you
agree with the author
about what Mondrian’s
shapes and colors
express? Explain why
or why not
Reading
Strategy
Composition in Red, Yellow,
and Blue Mondrian painted
this work in 1942 There are many golden rectangles in this painting.
Composition in Red, Yellow,
and Blue This work was
painted in 1926 You can find
many golden rectangles here,
too.