000 03491cam a2200481Ii 4500
001 BRILL9789463006996
003 nllekb
005 20260610105519.0
007 cr un uuuua
008 190403s2016 gw sb 001 0 eng d
020 _a9789463006996
_q(electronic book)
020 _z9789463006989
_q(print)
024 7 _a10.1007/978-94-6300-699-6
_2DOI
035 _a(OCoLC)964657030
040 _aNL-LeKB
_cNL-LeKB
_erda
050 4 _aQA174.7.S96
072 7 _aJN
_2bicssc
072 7 _aEDU
_x000000
_2bisacsh
082 0 4 _a516.1
_223
100 1 _aSinitsky, Ilya.,
_eauthor.
245 1 0 _aChange and Invariance :
_bA Textbook on Algebraic Insight into Numbers and Shapes /
_cIlya Sinitsky, Bat-Sheva Ilany.
264 1 _aLeiden,
_aBoston :
_bBrill | Sense,
_c2016.
300 _a1 online resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_2rdacarrier
490 0 _aEducational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001
504 _aIncludes bibliographical references and index.
505 0 0 _aPreliminary Material -- The Concept of Invariance and Change: Theoretical Background -- Invariant Quantities – What Is Invariant and What Changes? -- The Influence of Change -- Introducing Change for the Sake of Invariance -- Discovering Hidden Invariance -- Change and Invariance in Geometric Shapes.
506 _aAvailable to subscribing member institutions only.
520 _aWhat is the connection between finding the amount of acid needed to reach the desired concentration of a chemical solution, checking divisibility by a two-digit prime number, and maintaining the perimeter of a polygon while reducing its area? The simple answer is the title of this book. The world is an interplay of variation and constancy—a medley of differences and similarities—and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes. After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter’s theme. Some examples: “How to represent all the integers from zero to 1000 using ten fingers?”, “How to win at the game of Nim?”, “Why do different square lattice polygons with the same area often have the same perimeter?”
650 0 _aSymmetry (Mathematics)
650 0 _aMathematics
_xStudy and teaching.
650 0 _aMathematical models.
650 0 _aAlgebra.
650 0 _aGeometry, Algebraic.
650 0 _aMathematics
_xPhilosophy.
700 1 _aIlany, Bat-Sheva,
_eauthor.
776 0 8 _iPrint version:
_tChange and Invariance: A Textbook on Algebraic Insight into Numbers and Shapes
_dLeiden, Boston : Brill | Sense, 2016,
_z9789463006989
830 0 _aEducational Research E-Books Online, Collection 2005-2017, ISBN: 9789004394001.
856 4 _zDOI:
_uhttp://dx.doi.org/10.1007/978-94-6300-699-6
999 _c38339
_d38339