Re: [Origami] Donovan Johnson's Paper Folding for the Mathematics class
Searching "Donovan A. Johnson" on the broadly interdisciplinary Google Scholar yields 112 references to the book, on teaching math. The 37 page pamphlet is readily available on the Internet Archive (2 versions) looking for Donovan A Johnson ( at https://ia801300.us.archive.org/22/items/ERIC_ED077711/ERIC_ED077711.pdf But searching Donovan A. Johnson on Google scholar, for example, leads to other interesting papers Title: A history of folding in mathematics http://gen.lib.rus.ec/book/index.php?md5=8BC61D7731DCC46DDA1A8A74D79DCEFF Author(s): Friedman.; Friedman, Michael; Goob Publisher: Birkhauser,Springer International Publishing Year: 2018 430 pages Table of contents : Content: Introduction. - From the 16th Century Onwards: Folding Polyhedra. - New Epistemological Horizons?. - Prolog to the 19th Century: Accepting Folding as a Method of Inference. - The 19th Century - What Can and Cannot be (Re)presented: On Models and Kindergartens. - Towards the Axiomatization, Operationalization and Algebraization of the Fold. - The Axiomatization(s) of the Fold. - Appendix I: Margherita Beloch Piazzolla: "Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row". - Appendix II: Deleuze, Leibniz and the Unmathematical Fold. - Bibliography. - List of Figures. and to the later and smaller version Title: A History of Folding in Mathematics: Mathematizing the Margins Volume: http://gen.lib.rus.ec/book/index.php?md5=1964A01DCFCC4E0412A41B9D49AF1CD0 Author(s): Michael Friedman Series: Science Networks. Historical Studies Publisher: Birkhäuser Year: 2018 Edition: 1st ed. 2018 "While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is ?2 with these instruments – the Italian mathematician Margherita Beloch Piazzolla's discovery in 1934 that one can in fact construct a segment of length [square root] of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few question immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics." == An Investigation Of The Effect Of Origami-Based Instruction On Elementary Students’ Spatial Ability In Mathematics A Thesis Submitted To The Graduate School Of Social Sciences Of Middle East Technical University By Sedanur Çakmak 133 pages http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.633.1841=rep1=pdf and Origami On Computer David Fisher 75 pages http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.74.8461=rep1=pdf (The PDF excludes any illustrations) - A History of Folding in Mathematics by Michal Friedman Individial chapters are on the Springer publisher site The chapter Coda First Online: 26 May 2018 has had 903 Downloads There are two versions of of the book on Library Genesis: 5.6 Mbytes and 10.4 Mbytes PDFs Friedman M. (2018) Coda: 1989—The Axiomatization(s) of the Fold. In: A History of Folding in Mathematics. Science Networks. Historical Studies, vol 59. Birkhäuser, Cham The DOI should get you lots of related items from Library Genesis and Sci-hub DOI https://doi.org/10.1007/978-3-319-72487-4_6 Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Setting the Scene: Which Instrument Is Stronger? . . . . . . . . . . . . . 1 1.2 Marginalization and Its Epistemological Consequences . . . . . . . . . 5 1.3 Marginalization and the Medium: Or—Why Did Marginalization Occur? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 The Economy of Excess and Lack . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Historiographical Perspectives and an Overview . . . . . . . . . . . . . . 19 1.5.1 Marginalized Traditions . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 The Historical Research to Date and Overview . . . . . . . . . 22 1.5.3 Argument and
Re: [Origami] Origami and axioms: 1957
> On 19 Jul 2020, at 18:41, Papirfoldning.dk via Origami > wrote: > > I got my copy of "Donovan A. Johnson: Paper folding for the mathematics > class" here: > https://www.amazon.com/gp/offer-listing/B003TV5BBK/ref=tmm_pap_new_olp_0?ie=UTF8=new=1595147259=1-1-791c2399-d602-4248-afbb-8a79de2d236f > I found it is also available from a government repository: https://files.eric.ed.gov/fulltext/ED077711.pdf Though I imagine a reprint would be much nicer, as the facsimile is rather noisy. For anyone else interested, the section Hans has introduced is in the introduction on page iii. All the best, Matthew
Re: [Origami] Origami Digest, Vol 171, Issue 16
- Mensaje de "Papirfoldning.dk" Thanks a lot, Hans, for sharing such an interesting discovery! Since O1-O7 are independent axioms, and O4 is Euclidean (you can construct a line through a point, perpendicular to another line), it seems that Donovan's postulates cannot construct all Euclidean constructs, despite his claim. I believe they actually can. On one hand, the manouvre described in O4 may be regarded as a particular case of O5, when the first point (the one you are moving, say P) belongs to the given line (say, l) thus, you are folding perpendicularly to l. So, you just need to choose ANY point of l to perform O4. So, in most of the theoretical settings I can imagine, you can do it by using the other axioms and something else. If your theory lets you use the axiom of choice (most of the formal settings for constructions do NOT), you are done. If you are using the axioms with an initial set consisting in two points (as it is customary), then you can construct two perpendicular lines (namely, Y=0 and X=1/2, in cartesian notation, if you started with (0,0) and (0,1)). At least one of those lines intersects the original line l and you are done. On the other hand, it is well known that the first five axioms O1-O5 give the Euclidean constructions (that is, using compass and ruler), if you have (0,0) and (0,1) as initial set. So, the "only" thing Johnson was missing is O6. All the best! ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ JOSE IGNACIO ROYO PRIETO Matematika Aplikatua Saila University of the Basque Country UPV/EHU Pza. Ingeniero Torres Quevedo, 1 48013 Bilbao SPAIN Phone: 00 34 946013987 FAX: 00 34 946014244 E-mail: joseignacio.r...@ehu.eus Web:http://www.ehu.eus/joseroyo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Re: [Origami] Origami and axioms: 1957 (Papirfoldning.dk)
Den 19. jul. 2020 kl. 10.04 skrev Matthew Gardiner : Do you happen to have a link to the publication? The whole text can be downloaded from ERIC site. Here's the link: https://eric.ed.gov/?id=ED077711 The introduction page is difficult to read because of the background texture. All the best. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ JOSE IGNACIO ROYO PRIETO Matematika Aplikatua Saila University of the Basque Country UPV/EHU Pza. Ingeniero Torres Quevedo, 1 48013 Bilbao SPAIN Phone: 00 34 946013987 FAX: 00 34 946014244 E-mail: joseignacio.r...@ehu.eus Web:http://www.ehu.eus/joseroyo ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Re: [Origami] Origami and axioms: 1957
> > This might be of some historical interest for origami and mathematics. I’d say it most definitely is! Very interesting find. > The usual set of origami axioms are acknowledged to be formed by > Huzita-Justin-Hatori (https://langorigami.com/article/huzita-justin-axioms/). Aha! So is it now Johnson-Hujita-Justin-Hatori axioms? JHJH is kind of symmetrical. > I've looked in Donovan A. Johnson: Paper folding for the mathematics class, > National council of teachers of mathematics, USA, 1957. Photographic reprint > 2019. I’d generally agree with your summation of the points, however, there’s others on the list with more authority and knowledge that can offer more substantial input. Do you happen to have a link to the publication? Thanks, Matthew Ps. Minor toot: I’m about to release a run of my new robotic origami kits: called oribokit :) There will be some available for postage internationally. More info soon.
[Origami] Members of ASVOR folding a crane
Hello. As a challenge, our origami group ASVOR (vallecaucanian origami association) in Cali, Colombia, folded a crane. Pass the paper and make a step. https://www.youtube.com/watch?v=x4RrLcfbPeU Jose Tomas Buitrago.
