THE DERIVE - NEWSLETTER #67 ISSN 1990-7079 THE BULLETIN OF THE USER GROUP C o n t e n t s: 1 Letter of the Editor 2 Editorial - Preview Nils Hahnfeld & Josef Böhm 3 Conics Made Easy 8 User Forum Josef Lechner 10 All bodies are falling equally fast? Albert Rich 19 A Repository of Mathematical Knowledge MacDonald Phillips 21 Actuarial Math on the Handheld Bernhard Kutzler 33 TI-NSpire-CAS = Successor of DERIVE!? David Sjöstrand 39 Points of Interest in a Triangle Johann Wiesenbauer 46 Titbits 34 – Polynomial Arithmetic for the Advanced Josef Böhm 51 Surfaces from the Newspaper (2) 53 First Announcement of TIME 2008 & another Conference September 2007 D-N-L#67 Book Shelf D-N-L#67 Nachhaltige CAS-Konzepte für den Unterricht Eberhard Lehmann Vorwort – Inhaltsverzeichnis 1. Der Start in das CAS 2. CAS-Konzepte 3. Hand contra CAS 4. Visualisieren und Animieren 5. Families 6. Modules (Bausteine) - modulare Kompetenzen 7. CAS-Projekte - Modellieren mit CAS-Hilfe 8. Mathematik mit und auf Bildern 9. Das CAS macht es möglich 10. Erstellen von CAS-Aufgaben – Klassenarbeiten / Klausuren / Hausaufgaben 12. Zentralabitur mit CAS 13. CAS-Werkzeugkompetenzen 14. Empfehlungen für ein CAS-Schulcurriculum Sammlung von CAS-Beispielen in dem Buch Sachverzeichnis Bestellung des Buches bei: Dr. Eberhard Lehmann [email protected], 030-7112420, www.snafu.de/~mirza 20 Euro + Verpackung/Porto auf Rechnung Another new publication is: Günter Scheu u.a., ABITUR – Prüfungsaufgaben mit Lösungen, Mathematik CAS, Gymnasium Baden-Württemberg, STARK Verlag If you know about CAS- related publications then please inform me. Books dealing with the use of technology in math education in general are also interesting. Josef D-N-L#67 LETTER OF THE EDITOR p 1 Dear DUG Members, Another gem is promised for one of the next DNLs: I am sorry for the delay delivering DNL#67. But I A. Perotti joined the DUG recently. I remembered believe that its contents is worth some days over- Alessandro´s article on Groebner Bases in an ear- time. We have again much more pages than the lier issue of the Intl DERIVE Journal. I wrote a usual 40 – 44 pages. I didn´t want to leave one of mail and he immediately answered. He has adapted the articles for the next issue. Josef Lechner´s con- his DOS-Derive functions for DERIVE6 and wrote tribution is one of the many ones which waited very a full paper. He gave permission to publish it in the long for publication, here it is at last. Nils Hahnfeld DNL and additionally promised to write an extra has been busy as ever and produced new packages introduction. So we can hope that solving systems for the handheld. As one of my final diploma pa- of nonlinear equations applying Buchberger´s algo- pers at university dealt with conics I was very in- rithm will not remain a „Black Box“ for some (or terested in his CME (Conics Made Easy). I could many?) of us. not resist making suggestions for including addi- You can also find a contribution from Don Phillips, tional features and a very intense communication bringing actuarial math on the handheld together has started. You can find a selection of this discus- with some additions for the former DERIVE file. sion together with a short presentation of CME. Peter Lücke-Rosendahl wrote a mail concerning Differential Equations Made Easy will be presented some „gaps“ in my DNL#15 contribution on Curve in a future DNL. Discussions. We had an interesting exchange of One highlight in this issue is doubtless Albert mails and files and I´ll come back to this issue in Rich´s visionary paper. I am very happy and proud the next DNL. that Albert like so many of you keep on communi- TIME GOES AFRICA. TIME 2008 will be held cating within the DUG. It would be great if DUG 22 – 26 September 2008 at Buffelspoort Resort, members would follow Albert´s invitation for sup- South Africa. porting his vision. Michel Beaudin and I were asked to act as Co- Another vision is to transfer as many Derive func- Chairs for the DERIVE-Nspire-CAS-strand. Michel tionalities as possible to its intended successor, the and I found it a good idea to have a completely new TI-Nspire. The TI-programmers promised to do group of colleagues in the Program Committee. We their best and they are asking for the DERIVE- would like to thank alle members of earlier PCs. people´s input. The DUG can play an important They did a great job and they really deserve a role in transfering the “DERIVE spirit“ to the break. Nspire. (Maybe it is not a pure chance that Derive SPIRit and NSPIRe have an important part of their You can find the first flyer and invitation (together names in common). Bernhard Kutzler presents a with another announcement) at the end of this more detailed view on the Nspire. Next releases DNL. should contain one or the other of the DERIVE- Finally I´d like to draw your attention to the pre- features. Bernhard will continue in the next DNL sented books (unfortunately only in German). If with a special example to demonstrate how the anybody of you knows about interesting publica- various applications of Nspire can cooperate. tions, then please let me know. At the occasion of a meeting with the TI- By the way, Michel Beaudin provided a paper full programmers some of us presented our most appre- of exercises for his students on the EMTS (in ciated Derive features, which we would like to have French). We will publish it in the next DNL. implemented in future versions of Nspire David (Have a also look on SketchUp – page 20!) Sjöstrand showed an excellent example of applying Best regards to you all the ITERATES-command. This and other interest- ing findings in a triangle are collected in David´s contribution in this DNL. He extended some ideas into 3D space (see next DNL). Download all DNL-DERIVE- and TI-files from http://www.austromath.at/dug/ http://www.bk-teachware.com/main.asp?session=375059 p 2 E D I T O R I A L D-N-L#67 The DERIVE-NEWSLETTER is the Bulletin Contributions: of the DERIVE & CAS-TI User Group. It is Please send all contributions to the Editor. published at least four times a year with a Non-English speakers are encouraged to contents of 40 pages minimum. The goals write their contributions in English to rein- of the DNL are to enable the exchange of force the international touch of the DNL. It experiences made with DERIVE, TI-CAS must be said, though, that non-English arti- and other CAS as well to create a group to cles will be warmly welcomed nonetheless. discuss the possibilities of new methodical Your contributions will be edited but not and didactical manners in teaching mathe- assessed. By submitting articles the author matics. gives his consent for reprinting it in the DNL. The more contributions you will send, the more lively and richer in contents Editor: Mag. Josef Böhm the DERIVE & CAS-TI Newsletter will be. D´Lust 1, A-3042 Würmla Austria Next issue: December 2007 Phone/FAX: 43-(0)2275/8207 Deadline 15 November 2007 e-mail: [email protected] Preview: Contributions waiting to be published Some simulations of Random Experiments, J. Böhm, AUT, Lorenz Kopp, GER Wonderful World of Pedal Curves, J. Böhm Tools for 3D-Problems, P. Lüke-Rosendahl, GER ANOVA with DERIVE & TI, M. R. Phillips, USA Financial Mathematics 4, M. R. Phillips Hill-Encription, J. Böhm Farey Sequences on the TI, M. Lesmes-Acosta, COL Simulating a Graphing Calculator in DERIVE, J. Böhm Henon & Co, J. Böhm Do you know this? Cabri & CAS on PC and Handheld, W. Wegscheider, AUT An Interesting Problem with a Triangle, Steiner Point, P. Lüke-Rosendahl, GER Overcoming Branch & Bound by Simulation, J. Böhm, AUT Diophantine Polynomials, D. E. McDougall, Canada Graphics World, Currency Change, P. Charland, CAN Precise Recurring Decimal Notation, P. Schofield, UK Solving an Optimization Problem with the TI-Nspire CAS, B. Kutzler, AUT Cubics, Quartics – interesting features, T. Koller & J. Böhm Logos of Companies as an Inspiration for Math Teaching Exciting Surfaces in the FAZ BooleanPlots.mth, P. Schofield, UK What is hiding in Dr. Pest? B. Grabinger, GER Truth Tables on the TI, M. R. Phillips Advanced Regression Routines for the TIs, M. R. Phillips Directing Our Suspicions with AHP, C. & P. Leinbach, USA Where oh Where is IT? (GPS with CAS), C. & P. Leinbach, USA Groebner Bases, A. Perotti, IT Embroidery Patterns, H. Ludwig, GER Inspheres and Exspheres of a Tetrahedron, D. Sjöstrand, SWE Compléments de mathématiques (profil Génie Mécanique), M. Beaudin, CAN and others Impressum: Medieninhaber: DERIVE User Group, A-3042 Würmla, D´Lust 1, AUSTRIA Richtung: Fachzeitschrift Herausgeber: Mag.Josef Böhm D-N-L#67 Conics Made Easy p 3 Conics Made Easy for TI-89/Titanium and TI-92+/Voyage 200 DUG-Member Nils Hanhfeld offers two new packages for the TI-handheld devices: CME (Conics Made Easy) and DME (Differential Equations Made Easy). Both products can be purchased via Internet: www.ti89.com. I´d like to present some screen shots from CME. I´ll take the Voyage 200 because of the larger screen which needs a lot less scrolling the screens. After loading the Flash Application you are offered a bar with 5 drop down menus. The first menu gives the most important information about the conics, eg. the ellipse: The most powerful menu is F2 Analyze. You can enter either the coefficients of the equation of a given polynomial (in rectangular coordinates only) or the full equation (see the example).