GeometriochmatematikenshistoriaInstitutionförmatematikochmatematiskastatistikManyaRaman-Sundström,lärareManya.sundstrom@umu.se Schema, HT 2016

Kursliteratur: Johansson, Bo Göran. Matematikens historia 2, Lund: Studentlitteratur : 2013: 540 s. (other editions of this book are also fine)WewillalsouseGeogebraforsomeoftheclassactivities.Seehttps://www.geogebra.org/m/h7Vq2G4g/Datum Tid Sal Ämne2/11 Kl9:15-11:30 MA356 KursIntro:Babylonien&Egypten(kap.1,2)4/11 Kl10-12 MA356 Grekland(kap3)8/11 Kl10-12 MA136 Pytagorassats(Aktivitet)10/11 Kl10-12 Ub335 Pappussats,Morleyssats(Aktivitet)**11/11 Kl10-12 MA356 Elementen(kap3)14/11 Kl16 Draftofprojectdue17/11 Kl10-12 Ub337 Taxicabgeometri&HilbertsAxioms(Aktivitet)18/11 Kl10-12 N370 Kina(Hist.4)22/11 Kl10-12 MA346 Indisk&Arabiskmatematik(Hist5-6)24/11 Kl10-12 MA356 Europaundermedeltiden(Hist7)25/11 Kl16 Writtenprojectdue28/11 Kl10-12 MA136 Reellatal,analys(Hist8-9)29/11 Kl10-12 N330 Hyperboliskochsfäriskgeometri(Aktivitet)**1/12 Kl9-12

(OBStid!)MA156 Studentpresentationer*

6/12 Kl13-16(OBStid!)

MA356 Studentpresentationer*

8/12 Kl13-16 MA356 Studentpresentationer*+Repetition12/12 Kl11-17 Exam (*)Obligatoryonthedayyoureview.(**)Bringlaptop.

http://www.bridgesmathart.org/art-exhibits/bridges06/sequin.html

ExaminationerTheexaminthiscoursewillconsistofaproject(whichhasawrittenpartandanoralpart)andanexam.Theprojectwilleitherbeahistorypaperoralaboratoryaimedattheschoollevel.Draftsoftheproject,maximum2pages,aredue14/11andfinalversions,maximum6pages,aredue25/11.Oralpresentationsforbothpapersandlaboratorieswillbegiventhelastweekofclass.Paperpresentations(individual)willlast10minutes,andlaboratories(groupsof3students)willlast30minutes.Theexamwillcoverinformationfromtheentirecourse,includinginformationfromthebook,lectures,andclassroomactivities.GradingTotalnumberofpointspossibleis4points(writtenproject)+2points(oralproject,consistingof1pointforpresentationand1pointreviewinganotherpresentation)+12points(writtenexam)=18points.ToearnGincourse,oneneeds10points,ofwhich4mustcomefromtheproject.ToearnVGincourse,oneneeds14points,ofwhich5mustcomefromtheproject.Language:TheclasslanguageisSwedish,thoughcoursematerialsmaybeinEnglish.AllexamsmaybewrittenineitherEnglishorSwedish.References: All history projects, both the essays and the laboratories must be properly referenced. Any sign of plagiarism, using someone else’s work either in whole or in part, could result in failing the course. Suggestedhistorytopics(youarewelcometochooseyourown):Aristarchus: Who was he? How did he find the distance from the sun to the moon? http://www.astro.cornell.edu/academics/courses/astro201/aristarchus.htm History of negative numbers: https://nrich.maths.org/5961 History of infinity. How was infinity described in Jain mathematics (2nd and 3rd century BC). In other cultures? How is it understood today (including Cantor’s diagonalization argument.) Where and when did the Pythagorean theorem really originate? Warning--- this is a hard question, historians claim different things. History of function: Why is the concept of function defined how it is today? http://www.mr-ideahamster.com/classes/assets/a_evfcn.pdf What have women contributed to the history of mathematics? Pick a woman and talk about her contributions and life story.

https://en.wikipedia.org/wiki/List_of_women_in_mathematics A brief history of logic. What features of modern logic are similar and different to ancient logic. http://plato.stanford.edu/entries/logic-ancient/ Whatisthedimensionoftheuniverse?Historyofthisquestion.Suggestedlaboratories(youarewelcometodesignyourown):Counting in the ancient Mayan culture. The background should include: Where did it come from, how does it work, and when was it supplanted by modern methods? http://www-history.mcs.st-and.ac.uk/HistTopics/Mayan_mathematics.html Paul Erdős, who was he and what were some of his favorite problems that could be accessible to high school students? https://erdos.sdslabs.co/problems/111 Knot theory, Braid theory: What are the central questions, who were the people involved, and why do mathematicians care about these topics? http://www.cut-the-knot.org/do_you_know/knots.shtml and http://www.math.ucla.edu/~radko/191.1.05w/erin.pdf Sphere packing problem (Kepler’s conjecture): https://en.wikipedia.org/wiki/Sphere_packing The Leibniz-Newton calculus controversy https://en.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calculus_controversy What is the difference between a parabola and a caternary? What is the history of both of these curves? https://en.wikipedia.org/wiki/Catenary_arch

’ Fromhttp://discoveringegypt.com/egyptian-hieroglyphic-writing/egyptian-mathematics-numbers-hieroglyphs/