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Geometry in gardens and parks

Gabriela Pavlovičová, Lucia Rumanová and Valéria Švecová

1 Introduction

Development of children’s perception of geometric content is related with environment where early age children are brought up and gain everlasting and informal knowledge. It is important to combine the knowledge with real life situations. This can be done by solving applied mathematical problems developing pupil’s independence, activity and creativity from lowest grades of elementary school. By solving applied mathematical problems pupils should be able to verbalize problems, find missing information to solve problems, make relations and be able to formulate and interpret results. When developing tasks, we focused on increasing pupils’ motivation to problem solving. We were inspired by beautiful gardens and parks as a rich source of geometrical objects. Solving the tasks, pupils also develop spatial imagination and apply already acquired knowledge on geometry. For task development pictures and photographs of modern and historical gardens and parks are inevitable. The tasks are divided according to used context: x x x x geometrical shapes in parks and gardens, symmetry in parks and gardens, mazes in parks and gardens, measure in parks and gardens.

Introduction of each thematic unit includes tasks with identical solution, but different assignment: standard assignment and assignment motivated by geometry in gardens and parks. Individual thematic units may overlap and existing images may be used in different tasks. All tasks represent open problems with more than one solution, and may be continuously modified with current didactic situations. We can motivate pupils by giving problem and this motivation is challenge for creativity.

2 Geometrical Shapes in Parks and Gardens

Tasks in this thematic unit are aimed to determine, sort and identify basic characteristics of geometric shapes. Individual shapes are depicted in the images of gardens and contribute to creativity and imagination of pupils. TASKS FOR COMPARISON 1 The standard problem 1 The application problem 1

What geometric shapes can be found in the Eva wants to decorate fabric according to a picture after splitting the object into different picture of garden in India. While drawing one parts or joining the individual parts? part of the square paper she realized that the picture can be divided into several geometric shapes which would make her work easier. Can she get regular geometric shapes by dividing or joining parts of the image?

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Fig. 1

Fig. 2 Geometric patterns in Anguri Bagh garden, Agra Fort. Agra in India

Problem 1 In Kroměříž Flower Garden we can find various geometric shapes. Which geometric shapes are in the picture? How many shapes can you find?

Fig.3 The garden in Kroměříž (Czech Republic) was built by Italian architects, Filibert Luches and Giovanni Pietro Tencalla in 17th century. Gardens are enlisted as a UNESCO World Heritage Site Problem 2

Landscape architect C.Th. Sørensen designed a special type of a garden where various geometric shapes are arranged in certain geometric order. What types of geometric shapes is this garden made of? What is the relation between each polygon side length? Which polygon is next in order?

Gardens, lemonade, space shuttle and others have a common denominator

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Fig.4 The Geometric Gardens - a complex in Herning, West Jutland (Denmark), 1983 designed by landscape architect C.Th. Sørensen for another site and later realized at Herning by the Committee for the Geometric Gardens. Problem 3 Peter admired the work of Nannett Richford who designed the garden in the picture. He counted all triangles and squares in the picture. How many did he find? How many circles can he form out of various parts of the garden?

Fig.5 Knot Garden design by Nannette Richford

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