New Shapes of Meaning is a project-based curriculum scroll for teachers and self-guided interdisciplinary learning. The first iteration was produced for Nevada Museum of Art & Desert Research Institute’s Science Alive Teacher-training Conference at Nevada Museum of Art in 2017.
AUDIENCE:
K-12+
TIME:
1-3 hours, variable.
STEAM SUBJECTS:
ART, MATH & [LIFE] SCIENCE.
This curriculum scroll contains YouTube Videos & other embedded material subject to copyright, and is intended for educational use only.
LET’S PLAY.
You’ve been given a white ‘design board’ & 6 square pieces to work with, each a different color.
Now, let’s play with the squares:
Arrange the squares on your design board,
into a rectangle.
Two Constraints:
1) None may overlap.
2) Neither of the two smallest may be placed along the outside edge (perimeter).
POSSIBLE DESIGNS/CONFIGURATIONS
Your design should look like one of these…
Describe what is happening, visually.
Did you place the squares in any kind of order?
How many rectangles can you locate in your design?
GOLDEN RECTANGLES
Interpret the visual/spatial meaning of the math equation below:
The above rectangle (a+b) is a golden rectangle, known as the Greek letter phi. It exhibits a special form of self-similarity.
The whole has the same shape
as one or more of the parts.
Phi can be represented:
Graphically (see above).
And/or logically: a+b is to a, as a is to b.
And/or as number; approximately equal to 1.618…
This idea grows.
If the dimensions of the smallest squares are 1x1 inch, what are the dimensions of the 4 remaining squares?
____ x ____ in.
____ x ____ in.
____ x ____ in.
____ x ____ in.
If we continue to build out the design, what will be the dimensions of the next largest square?
____ x ____ in.
How did you make your prediction?
Let’s recap:
The two smallest squares are 1 in .x 1 in.
The 4 remaining squares are:
2 in. x 2 in.
3 in. x 3 in.
5 in. x 5 in.
8 in. x 8 in.
If we continued to build out the design, what would the dimensions of the next largest square be?
13 in. x 13 in.
Predict again:
Were this design to continue to expand, where would the next square (at 21 in. x 21 in.) be placed in the design?
WHAT IS A SEQUENCE?
In mathematics, a sequence is an enumerated collection of objects. It can be thought of as a list of elements with a particular order.
Is there a numeric sequence to these numbers?
EYE SPY A SEQUENCE!
The Fibonacci Sequence
A Fibonacci sequence of numbers is one in which each number is the sum of the two preceding ones,
starting from 0 and 1.
0+1=1
1+1=2
2+3=5
3+5=8
5+8=13
8+13=21
…0,1,1,2,3,5,8,13,21,34…
THE FIBONACCI SEQUENCE
A BRIEF HISTORY
The Fibonacci Sequence is a sequence of numbers. every number is the sum of the two previous.
While It is named after the Italian mathematician and merchant, Leonardo of Pisa, commonly known as Fibonacci, the history of the sequence goes as far back as 200BC.
Indian mathematics as early as 200 BC, in work by Pingala looked for possible patterns in Sanskrit poetry, formed from syllables of two lengths.
another 1400 years passed before Fibonacci published on the subject, with Liber Abaci, published in 1202, which introduced the sequence to Western European mathematics by demonstrating its use in a thought experiment, pertaining to reproduction in imaginary raBbits & bees.
While the history and cultural references derived from the sequence are fascinating - it is the nature of the sequence itself; the idea alone that is most Remarkable. the sequence of numbers abides and produces what is known as a golden spiral - an expanding form, with a spacial relationship that mirrors the cosmos and even our daily lives. our relationship with the this mathematics is not just reflected in nature, it is the shape of it.
“The human mind always makes progress, but it is a progress in spirals.”
Madame de Stael
PREDICT & ENVISION
GOLDEN SPIRALS
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
PREDICT/Envision
The above design shows a white line running diagonally through the purple square…
What is the correct path for this line to continue along, in order to express an ever growing spiral?
Fibonacci Spirals are Golden Spirals
Now watch this, it’s fantastic too.
DOODLING IN MATH
Golden Spirals, from scratch.
Construct
triangles from the squares, by folding them diagonally.
Arrange
the triangles in the shape of a Golden spiral.
Create
a spiral from positive or negative space.
Fibonacci snail, by Ottilie Allen, 3rd Grade.
SNAIL? WAVE? SHELL?
One more flick!
BLOOMS
Does a spiral have a New Shape of Meaning - for you?
Check out my project MindSETS too.
And reach out with feedback to aallen@alpineacademy.net.
Stay tuned!
Up next: Fibonacci Trees, Bees & Bunnies
Thanks for scrolling along with me. Until next time.
