By Harold Abelson;Andrea diSessa
Turtle Geometry offers an leading edge application of mathematical discovery that demonstrates how the powerful use of private desktops can profoundly switch the character of a student's touch with arithmetic. utilizing this ebook and some uncomplicated laptop courses, scholars can discover the houses of house through following an imaginary turtle around the monitor. the concept that of turtle geometry grew out of the brand workforce at MIT. Directed by means of Seymour Papert, writer of Mindstorms, this workforce has performed large paintings with preschool young children, highschool scholars and collage undergraduates.
Read or Download Turtle Geometry: The Computer as a Medium for Exploring PDF
Best geometry and topology books
The geometry of actual submanifolds in advanced manifolds and the research in their mappings belong to the main complex streams of latest arithmetic. during this region converge the thoughts of varied and complex mathematical fields corresponding to P. D. E. 's, boundary worth difficulties, caused equations, analytic discs in symplectic areas, complicated dynamics.
Designing fair curves and surfaces: shape quality in geometric modeling and computer-aided design
This cutting-edge examine of the thoughts used for designing curves and surfaces for computer-aided layout functions makes a speciality of the primary that reasonable shapes are regularly freed from unessential gains and are uncomplicated in layout. The authors outline equity mathematically, display how newly constructed curve and floor schemes warrantly equity, and support the consumer in making a choice on and removal form aberrations in a floor version with no destroying the imperative form features of the version.
- Combinatorial and Geometric Structures and Their Applications
- Éléments de Mathématique: Topologie Generale 5-10. Chapitres 5 a 10
- On the topological classification of certain singular hypersurfaces in 4-dimensional projective space
- Geometrical Researches on the Theory of Parallels
Additional resources for Turtle Geometry: The Computer as a Medium for Exploring
Example text
Then assigning to the pair (t, τ ) the pair (α(t, τ ), β(t, τ )) defines a map Cfg : St1 × Sτ1 → Sα1 × Sβ1 between two tori. e. to the number 4deg(Cfg ). The proof of this claim is given by the following observations. 1. e. when the point (t, τ ) belongs to the pre-image of one of the points (0, 0), (0, π ), (π, 0), (π, π ). 32 1 Elements of homology theory β g(τ ) α f (t) Figure 24. Assignment to the pair (t, τ ) of the pair (α, β). 2. The points (0, 0), (0, π ), (π, 0), (π, π ) are regular values of the map Cfg .
Many theorems that are quite complicated in the simplicial theory become very simple in the singular one. For instance, the theorem on isomorphism of the homology groups of homeomorphic spaces is trivial in the frame of the singular theory. 15 Lefschetz fixed point theorem 47 disadvantages of the singular homology groups are the difficulty of calculating them and the psychological discomfort of operating with infinitely generated groups. 15 Lefschetz fixed point theorem Let f : K → K be a simplicial map from a simplicial complex K to itself.
Its homology groups are denoted by Hn (K; G) and are called the homology groups of K with coefficients in G. The further construction of the homology theory with coefficients in G does not differ from the case of integer coefficients.