This PREP workshop was made possible by the NSF grant DUE: 0341481

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Folks going to MathFest?

I'm not sure what is the best place to do this, but I'd love to know if any of you are going to be at MathFest later this summer. Perhaps we could get together and talk about math and art! I (Angela) will be there early attending the short course and then through Friday I think, and I'll be giving a talk on game theory and division of labor in parenting on Thursday. Angela 14:30, 27 June 2008 (UTC)

Euler's harmonic formula and a request for references

1) Does anyone have a good reference for spherical excess? 2) For polyhedron deficit beyond Wikipedia 3) has anyone ever seen the Euler harmonic formula: 1/E=1/D+1/S-1/2 where D=degree of a vertex, S=#of sides in a regular polygon and E=#of edges Works in a regular polyhedron or a regular tessealtion and illustrates many of the properties.I also like the form of the equation,realy a harmonic Euler's equation. Steve

A really nice reference for spherical excess (and hyperbolic defect) is David A. Singer, "Geometry:Plane and Fancy" (1998), a Springer Undergraduate Text in Mathematics. Not only does it do that, but it does tessellations in the three geometries.Bryan 04:16, 1 July 2008 (UTC)

Alternate Frieze Pattern Notation

In case anyone is interested, I am familiar with an alternate frieze pattern notation that I believe is a bit simpler to memorize than the longer form used in the Wiki.

The seven frieze patterns are 11, 1m, 12, 1g, m1, mg, and mm.

Recognizing them is relatively easy:

Question 1: Does the repeated motif have vertical symmetry?

If "yes", the first letter is "m".

If "no", the first letter is "1".

Questions 2: Does the repeated motif have horizontal symmetry?

If "yes", the second letter is "m". If not,

Does the repeated motif have glide symmetry?

If "yes", the second letter is "g". If not,

Does the motif look the same upside down (does it have rotational symmetry)?

If "yes", the second letter is "2". If not,

Did you answer "no" to the above three questions?

If "yes", then the second letter is "1".

I found examples of 11, 12, 1m, mg, and mm on the page of Maori patterns. (I couldn't find 1g or m1 in the Maori file). Look at patterns #14, 15, 19, 23, and 28. Can you use my explanation above to match the Frieze Pattern with the Maori ornaments?

(coulnd't figure out how to attach the actual pictures. Maybe someone nice will do it for me.) --Bill 23:31, 23 June 2008 (UTC)

Note btw that this different notation is descibed in one of the explorations. See escherwiki:Identifying Frieze Patterns Exploration Barta 03:30, 25 June 2008 (UTC)

Welcome

Welcome to the main discussion page for the PREP Geometry and Art Workshop. Post questions and answers on this simple bulletin board. Use a leading colon character to indent replies, and remember to sign your posts with four tildes (~~~~) which will automatically convert to your name and the current time. Bryan 04:18, 10 June 2008 (UTC)

A comment about posting: You can click on "edit" at the top of the page. This will put you in edit mode. Answering or joining a thread in the discussion is as easy as just typing in your answer below the text you're commenting on. If there is a new topic you would like to start, then type in a heading flanked by two "=" signs.
Just as "Welcome" is flanked by == == a couple of lines above (you can only see the formatting in edit mode). Barta 11:32, 10 June 2008 (UTC)

PREP 08 Geometry and Art News: June 10, 2008

Hello, and welcome to the MAA PREP 08 Workshop on Geometry and Art! This email, from Anneke and Bryan, is our first official greeting, and will give you a quick overview of the resources we'll be using during the workshop. This newsletter and much more is available from the main website for the workshop, the "PREP Wiki", at:

http://math.slu.edu/prep08

The workshop meets online June 23-27, with two 1.5 hour blocks each day from 10-11:30am and 2:30-4pm (Central Daylight Time).

The online portion has two main components, the PREP Wiki and our Wimba virtual classroom.

We will be using the PREP Wiki in three ways:

  • As a bulletin board for distributing information
  • As a discussion board for off-line discussion (when we're not meeting "live")
  • As a collaborative tool for creating course material.

In a follow up email, you'll receive your account on the PREP Wiki, which allows you to log in and edit pages. We'd appreciate it if everyone logs in and tries a little editing. Post something on the discussion board, and create your own user page with a picture, brief bio, a link to your home page, and some of your goals for the workshop. More detailed instructions will follow in the email with your password.

The Wimba virtual classroom will handle our 1.5 hour "live" blocks. It provides:

  • Video and audioconferencing
  • Collaboration tools (a multi-user "blackboard")
  • Text chat
  • Breakout "rooms" for small group work.

We will have two live testing sessions of Wimba to make sure everyone can use the site before the workshop begins:

  • 10am-12 (CDT) Thursday, June 12
  • 1-3pm (CDT) Monday, June 16

Please "atttend" one of these (for about 10-20 minutes, at any point during the session). We'll post a phone number on the PREP Wiki that you can call for help during these times. This gives us (and you) time to work out any technical issues, so we can have a productive first meeting.

In the next day or two, you will receive your account on Wimba along with detailed instructions. For now, you may run the software/hardware setup at our Wimba site: http://208.185.34.154/launcher.cgi?room=Math_Conference (there's also link on the PREP Wiki front page).

Your computer will need a microphone and speakers, or better still a headset. We'd like to try small group videoconferencing, so please try to find/borrow/buy a videocamera or webcam compatible with your computer. Past workshop attendees have reported that using a pair of computers can be useful, with one dedicated to the virtual classroom and the other for work on the side, but that's certainly not necessary.

Finally, there is a list of suggested reading on the PREP Wiki. None of these books are required - we'll distribute excerpts electronically as needed. However, you might want to check your library (or interlibrary loan) for them to use as reference material.

We'll be in touch almost every day from now until the workshop begins.. please don't hesitate to ask questions via email, or better still by using the PREP Wiki discussion board.

Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 12, 2008

This morning from 10am-12 (CDT) we'll have the first of our two scheduled tests of our online classroom system Wimba, with the other test on Monday from 1-3pm (CDT). Showing up for 10-20 minutes of either session should be enough time to get your system working smoothly.

The easiest way to reach our Wimba classroom is via the prominent link on the main page of the PREP Wiki at: http://math.slu.edu/prep08 Alternately, you can go to the Wimba classroom directly via the ugly URL: http://208.185.34.154/launcher.cgi?room=Math_Conference

At the Wimba site, you'll be prompted to log in as a participant. There is no special account name or password, just pick the name you want to use in class and log in. The first time you do this, you'll be prompted to run a brief (1-2minute) setup procedure that will test your web software and audio input/output.

If you have problems, you'll be able to reach us by phone. Check the PREP Wiki page for the number - unfortunately I haven't got it at hand.

It's good to see a few of you signing on to the PREP Wiki and making some edits. Hopefully everyone received their account and password. This Wiki is a tool for everyone in the workshop, so be bold - if you see something that's wrong or have a useful change, go ahead and edit it yourself.

Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 16, 2008

Wimba Classroom

This afternoon (Monday 6/16) from 1pm-3pm (CDT) we'll have the second of our two scheduled tests of our online classroom system Wimba. Showing up for 10-20 minutes of either session should be enough time to get your system working smoothly.

The easiest way to reach our Wimba classroom is via the prominent link on the main page of the PREP Wiki at: http://math.slu.edu/prep08 Alternately, you can go to the Wimba classroom directly via the ugly URL: http://208.185.34.154/launcher.cgi?room=Math_Conference

At the Wimba site, you'll be prompted to log in as a participant. There is no special account name or password, just pick the name you want to use in class and log in. The first time you do this, you'll be prompted to run a brief (1-2minute) setup procedure that will test your web software and audio input/output.

If you have problems, you'll be able to reach us by phone at 314-681-8752 during the test.

PREP 08 Geometry and Art News: June 19, 2008

Wimba Tests

The Wimba testing went very well. If you haven't tested your setup or are still having trouble, make sure the organizers know soon so that we can have everyone working by Monday.

Pre-workshop Questionnaire

Please remember to fill out the pre-workshop questionnaire and return directly to the PREP workshop evaluator, Barbara Edwards, by email at: edwards@math.oregonstate.edu You might recap some of your answers on your PREP Wiki user page so that the organizers and other participants can learn your interests.

PREP Wiki

Most of you have begun using the PREP Wiki by creating your user page and testing the user talk facility. Now is the time to browse the pages of other participants and start to 'meet' the group.

Math & Escher Wiki

Eventually, you'll be getting a (separate) account on the Math & the art of Escher wiki. The Escherwiki is a separate system from the PREP Wiki, and has more structure set up for creating and editing mathematical course content. Once we gain familiarity with wiki usage, we'll want to use the Escherwiki for more polished work. You're also invited to collaborate on the Escherwiki project. If you'd like an Escherwiki account right now, let Bryan know.

Small Groups

During the workshop, participants will frequently break into small groups of 3-4 people. We'll be putting the groups together this weekend, making some attempt to put people with common interest into the same group. Let us know promptly if you have any requests.


Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 24, 2008

Wiki Contributions

On Monday, we began creating math and art course content with group work on a list of artists. There are some interesting improvements and new pages to look at as participants continued to work after the sessions. It's worth taking a look at:

If you've got something cool we didn't notice, go ahead and mention it on the Discussion Page.

Here are photos of tile patterns in buildings Tile Patterns in Buildings I have also put up photos of student projects (not my students) Student Projects Virginia 19:26, 24 June 2008 (UTC)

Archives and Slides

Wimba archives from Monday are available on the Wimba Archives page. Presentation slides are available as well - go to the appropriate content page. For example, there are slides posted on Teaching Symmetry.

Technical Issues

As the week goes on, things should become routine. Even between the morning and afternoon, it seemed like people had fewer technical issues to deal with. Remember you can call 314-681-8752 if you are completely unable to connect and want to talk to one of our tech guys, Jeff or Dan.

One thing we're trying to fix on this end was the problem with 'Database Errors'. We'll try again with new hope tomorrow.

Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 25, 2008

Homework

No homework on Tuesday? Well, there should have been! On Friday, we'd like to take a virtual field trip of the mathematics in your home town.

Please try to find or take pictures of mathematics in your town. You might find mathematics in public art or sculpture, architecture, natural phenomenon, museum holdings, or many other places. If you've got a picture, upload it to the Virtual Field Trip page on the wiki.

Guest Presenter

This afternoon, we are privileged to have Thomas Banchoff of Brown University as a guest presenter (for the first 20 minutes or so). He is planning to talk about the art of Salvador Dali.

Breakout Groups

So far, you have all stayed in the same groups throughout. Because the online format is a bit awkward, we've kept people together to try and achieve some level of comfortable discourse. Question: Should we stir up the groups for the second half of the workshop? At this point, we are inclined to stay with these groups until the end, but we'd would like to hear opinions.

Wiki Contributions

There are too many new contributions to list! To provide a central source for your work this week, we've created a new page, Participant Contributions, with a more-or-less organized list of projects and worksheets being developed during the workshop. If you've got something cool we didn't notice, go ahead and add a link on the page.

Please see what your colleagues are doing - it's becoming an excellent resource. You are encouraged to collaborate, or simply to discuss what's been done. For every page on the wiki, there is an associated "Discussion" page, and we encourage you to use these.

Archives and Slides

Wimba archives from Tuesday are available on the Wimba Archives page. Presentation slides are available as well - go to the appropriate content page.

Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 27, 2008

Group Picture

A few of you still need to post (or email) your photo if you want to be in the group picture (and believe me, you do!) You have until a little after the morning session if you want to make the cut.

Math & The Art of M.C. Escher Wiki

If you'd like an account on the Math & Escher Wiki, send a note to Bryan. Many of you have asked for accounts, and should have received usernames and passwords via email. We are very excited to welcome you to the project. Don't be afraid to edit and add to the Math & Escher Wiki, because it is meant to be an open project. But please read the Policies and Guidelines for Editors page ( http://euler.slu.edu/escher/index.php/Policies_and_Guidelines_for_Editors ) first.

Post-workshop Questionnaire

There is a post-workshop questionnaire that the MAA PREP directors require all participants to complete. You will receive it by email after the workshop (or check the Discussion Page on the wiki).

Archives and Slides

Wimba archives from Wednesday and Thursday are available on the Wimba Archives page. Presentation slides are available as well - go to the appropriate content page.

Cheers, Anneke and Bryan

PREP 08 Geometry and Art News: June 30, 2008

Thanks

Anneke & I would like to thank all of you for making this a successful workshop. We were so impressed with your dedication and the quality of the materials you developed during the workshop. Trying to work in this strange new online environment was challenging, and it was fascinating to see the evolution from day one awkwardness to fluid collaboration by the end of the week. Your enthusiasm and good cheer really meant a lot to us. Also, we'd like to acknowledge all the behind-the-scenes help we got from Jeff Abernathy and Dan Shown, our technical support, and from Aileen Murphy, our graduate student helper.

Post-workshop Questionnaire

There is a post-workshop questionnaire (File:Post-questionnaire.pdf) that the MAA PREP directors require all participants to complete. It is attached to this email and also posted on the wiki. Please return it directly to Barbara Edwards (edwards@math.oregonstate.edu), the MAA coordinator for this workshop. Also, we (the organizers) will only receive a synopsis of the questionnaires. If you have comments or suggestions for improving this (or any) online workshop that you'd like us to hear, either send them via email or post them on the wiki discussion page.

Keeping In Touch

If you want to get in touch with someone from the workshop, remember that changing a participant's talk page will automatically email them with a note. Attached to this email is a list of all participant names and email addresses. This list will not be posted on the wiki.

Wiki Stuff

All Wimba archives are available on the Wimba Archives page. The remaining presentation slides will be posted shortly - go to the appropriate content page. We'll be working on collecting references in a more useful form (as well as finding a few more). This may take some time.

Workshop Follow-up

Over the course of the next year, the MAA and the organizers encourage participants to:

  • implement workshop-created activities in their own classrooms
  • continue the on-line discussion, sharing their experiences in the classroom
  • disseminate materials they develop both within the participant group, and also to the wider mathematics community

Please do come back and let us know how things are going. We may contact you from time to time in the next year as part of the MAA's assessment process for PREP workshops.

This will be the final "news" from the workshop. We wish you all success in your courses, and in all your future endeavors!

Anneke and Bryan

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