Home page | ## Discovering Euler’s formula on Polyhedrons< BE C eab- E Please publish or preview this page to view this custom HTML xml="true" ns="urn:schemas-microsoft-com:office:office" prefix="o" namespace=""> Welcome to re discover Euler’s formula, which had fascinated mathematicians for a long period of time. This formula giving a relationship between the vertices, edges and faces of a solid had inspired the great mathematician Lakatos of the 20
You have to have a basic knowledge of polygons and their properties as a pre requite skill before doing this activity. Also refer to a mathematical dictionary to know about a polyhedron, its vertices, edges and faces. And all you have to do now, is to follow instructions to make a polyhedron(prisms and pyramids), count the number of vertices, edges and faces, tabulate them, analyze and find a relationship between them.
Build two congruent triangles using the marshmallows and the spaghettis. Keep them parallel to each other and connect them using 3 spaghettis that are 6 cm long. < BE C eab- E Please publish or preview this page to view this custom HTML xml="true" ns="urn:schemas-microsoft-com:vml" prefix="v" namespace="">
Build two congruent rectangles using the marshmallows and the spaghettis. Keep them parallel to each other and connect them using 4 spaghettis that are 6 cm long.
Build two congruent pentagons using the marshmallows and the spaghettis. Keep them parallel to each other and connect them using 5 spaghettis that are 6 cm long.
Continue the same procedure to build a hexagonal prism, a heptagonal prism and an octagonal prism.
Build a triangle with the marshmallows and the spaghetti sticks. Poke 3 spaghettis of the same lengths on to the 3 marshmallows of the triangle and connect them at the top by bending them towards the center using another marshmallow.
Build a square with the marshmallows and the spaghetti sticks. Poke 4 spaghettis of the same lengths on to the 4 marshmallows of the square and connect them at the top by bending them towards the center using another marshmallow.
Build a pentagon with the marshmallows and the spaghetti sticks. Poke 5 spaghettis of the same lengths on to the 5 marshmallows of the square and connect them at the top by bending them towards the center using another marshmallow. Continue the same procedure to build a hexagonal pyramid, a heptagonal pyramid and an octagonal pyramid. Now use your constructions to record the number of vertices, edges and faces of the various prisms.
Congratulations if you were able to find a relationship between the vertices, edges and faces of a polyhedron. If you have not, or if you want to learn more about Euler’s formula, visit Euler's formula |