MATHS FLOWERS
“ We have in our minds a tendency to accept symmetry as some kind of perfection. In fact it is the old idea og the Greeks that circles were perfect and it was rather horrible to believe that the planetary orbits were not circles, but only nearly circles The difference between being a circle and being nearly a circle is not a small difference; it is fundamental change so far as the mind is concerned… Then the question is why it is only nearly a circle- that is a much more difficult question… So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why” Richard P. Feynman
Nature has covered the earth with an endless variety of shapes, the most fascinating of which have always been the most basic and most fundamental: the symmetry of a perfectly formed orange, a five-pointed starfish, a honeycomb polygon, an oval egg.
To biologists, each natural shape seems somehow unique, but to a mathematician, they are but a close representation of a true circle, or star, or oval, or hexagon. For centuries, biology and mathematics have existed on separate planes – geometry defined precise formulas for creating a circle, square, star, or any other shape; yet in nature, there is no true shape because all natural shapes are inexact.
Modeling process using shapes proceeds on successive steps to create a dynamic interaction between Nature’s World and Mathematics’ World. So MATHS FLOWERS born.
In it we wish to study geometric figures :circles, straight-lines, parabola, ellipse, hyperbola and other geometric curves to build flowers’ shapes, and above all we wish to introduce the Gielis ? SuperFormula. It is one mathematic formula throught it we can describe many flowers ‘shapes.
The age range of the pupils to be involved in the project : 16-18
Modality Working in the Project
Each partner in the twinspace has to partecipe in this activies:
- Cities and Schools: to make a short descriptions about partners ‘ cities and schools
- Learning in process : to upload partners ‘ photos during the activities in the different phases in the project.
- Maths Contents : in this activity partners describe streght-line, circle, parabola, ellipse and hyperbola definite in theoretical way (definitions, principal properties..).
- Flowers’ Images from each countries : to upload many images’collections about the flowers. Each partner can choose one or more flowers as symbols for own countries.
- Drawing by Cabri Geometre and Geogebra: in this activities streght-line, circle, parabola, ellipse and hyperbola were drawn by Geometric softwares: Cabri Geometre and Geogebra. There are theoretical files (how to construct geometric curves by Cabri and Geogebra) and consturction’s files (geogebra and cabri file extension). In it a short use’manual about Geogebra and Cabri Geometre uploaded too.
- Maths Flowers: each partner shall study the flowers as mathematical and geometric shapes and shall create an applet by using geogebra aor Cabri aor another different mathematical softwares. All new tools are welcome in the project.
MATHS FLOWERS project is a real growing up opportunity for the European students, because they can change experiences and find out new and different aspects about Nature’s World.
Aims in the project:
- to find out maths around us using maths language: geometry and algebraic curves
- to analyze nature’s shapes in mathematical point of view .
- to increase the use of the new tecnologies in the traditional didactic practice (Derive, Cabri Geometre, Geogebra)
- to make conjectures and individual simulations during the work.
- to compare different European education systems in maths
- to improve English language use in maths’s subjects.
- to feel the beauty of the world around us.
Methodology in the project:
a) to use digital photography to make a photo to flowers
b) to construct geometric shapes by using Cabri Geometre or GeoGebra or similar software
c) to superimpose the geometric construction to digital photography
d) to built a geometric patterns.
Maths Contents in the project:
- Cartesian geometry: streght-line, circle, ellipse, hyperbola, parabola
- Trigonometry: polar coordinates and polar equations about geometric loci
- Spiral curves
- Gielis’ Superformula
Final result in the project:
- To realize a blog to upload our principal phases of the project
- To realize a movie with partners in the project
This document is open and you can modify as you want.
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