# Yossi Elran

I'm a recreational mathematician and metagrobologist and head our institute's technology in education unit. I have a Ph.D. in theoretical quantum chemistry, and think math and science are really cool!

Location Rehovot, Israel

## Activity

• You're not thick at all @LeslyeSlater ... I take the blame for not explaining clearly enough. Thanks @LawrieBrown for doing a much better job than I have done...:-)

• Wow! Fantastic! @LawrieBrown

• Point flexagons are vertex flexagons... The pats hinge at the vertices of the triangles. Scott Sherman and others are working on a fundamental theory but it doesn’t look like it will involve group theory...

• + and -

• Yes - and in fact that has happened - Scott Sherman has found new flexes through his computer program!

• At a glance it looks correct! Good for you!

• Thanks for spotting that error !

• No - it's difficult to see the structure of the flexagon on picture 6 on the previous state - it has much more inner structure. The three sector fundamental first order square net can create two flexagons. One that in its main position is skewed (and doesn't lie flat), and the other that is a box. The net above has two sectors. The three sector version has a...

• Thanks @OlenaKryvtsun for spotting that error!

• The normal mode chart shows the states of the flexagons that are accessible without inverting the strip using the wormhole flex.
There is no special meaning to the letters, numbers or even order of columns and rows, except that the first four columns are states formed by twist flexing, the last four columns the patterns on the other sides, and alternating...

• LOL!

• The short answer is yes. But - to remove ambiguities - flexagons should be constructed with a stable main state. If, when they are first discovered, a more stable state is found when flexing, the flexagon construction instructions should be changed to make this new state the main state. Of course, in practice, this does not always happen...

• Good idea! They are theoretical, but, like many things, can be approximated by expanding the "point" connection to a very small linear hinge. I am not a great fan of vertex polygon rings, but I thought it important to include a mention of them so that if people encounter them, they'll at least have a clue of what they are.

• Thanks!

• Thanks @LornaAllen ! A good point... If I have time to redo them...

• @InekeFioole Thanks!

• @LeslyeSlater It should read "bottom leaf hinged to pat..." - try reloading or clearing the cache...

• Yossi Elran replied to David Webb

The answer is - not yet, really. But then, that's how many good inventions started...

• How very alert you are! :-) You are of course correct! Benjamin Franklin's magic squares - known as Franklin squares - do not add up to the magic number on the main diagonals - but they have other interesting properties which you can read about here: http://recmath.org/Magic%20Squares/franklin.htm

• My mistake... thanks for spotting that. I've corrected the text...

• Only by modifying the script language - this is beyond the scope of the course. However, the program should color the leaves "correctly" - though there is still some debate what "correctly" means on some of the more complicated flexagons...

• The main hinge is the hinge you are using for the flex. In some cases there are more than one - for example the pinch flex on the tri-hexa-flexagon. Because of symmetry in this case it doesn't matter which of the three you choose as the "main" one.

• Yes - you should receive an email with links to the recordings shortly @RuthEstrella-Pinto

• @InekeFioole Sorry to hear about your husband and thank you so much, not only for taking the course, but for being so active and stimulating so much conversation! Take care!

• Yes - you should receive an email with a link to the recordings shortly

• Yes!

• Making a video is a good idea - Thanks - I'll try to fit it in to my schedule.

• Thanks!!!!

• My pleasre @PaulC I'll be sending out an email with a link to the recordings later on this week

• There are two flexagon templates - one that turns into a heptagonal flexagon and the other a hexagonal flexagon - the numbering has no real meaning - just a way of indicating to those who downloaded or bought the full booklet which template we're using...

• There are a few posts on Facebook... Not many people on the course seem to use social media but don't let that put you off... :-)

• Yes - my mistake - thanks for spotting that - I've fixed it...

• @LeslyeSlater We'll have about up to 45 minutes...

• Yossi Elran made a comment

So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am Israel time (8:00 in London, UK, 9:00 in Madrid, Spain, 17:00 in Sydney, Australia). The other at 21:00 Israel time (14:00...

• Yossi Elran made a comment

So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am Israel time (8:00 in London, UK, 9:00 in Madrid, Spain, 17:00 in Sydney, Australia). The other at 21:00 Israel time (14:00...

• Yossi Elran made a comment

So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am Israel time (8:00 in London, UK, 9:00 in Madrid, Spain, 17:00 in Sydney, Australia). The other at 21:00 Israel time (14:00...

• Yossi Elran made a comment

So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am Israel time (8:00 in London, UK, 9:00 in Madrid, Spain, 17:00 in Sydney, Australia). The other at 21:00 Israel time (14:00...

• Yossi Elran made a comment

So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am Israel time (8:00 in London, UK, 9:00 in Madrid, Spain, 17:00 in Sydney, Australia). The other at 21:00 Israel time (14:00...

• So I've reread all your comments, and seeing as it seems that you have quite a lot of questions, by popular request I am happy to tell you that I have managed to arrange two more Zoom sessions this coming Thursday July 1st. One at 10:00 am...

• I really can't understand it then @SuzanneByrne... In my browser the template and the video are the same! Since the problem was with the video - can you perhaps pause the video and take a screenshot of each side and email it to me along with your downloaded template so I can try and figure this out? My email is: yossi.elran@weizmann.ac.il

• Yes!

• Sorry @PaulC @MurrayBelchamber @InekeFioole @LeslyeSlater @RuthEstrella-Pinto @LawrieBrown @SuzanneByrne @JohnSloman - I didn't have a chance to reply over the weekend. I was trying to locate the recording, which unfortunately I can't find anywhere... I'll keep on trying and if possible arrange another zoom...

• @MarkBooth @InekeFioole @RosemarieMiddleton I assure you - it NEVER happens as you expect the first few times you try flexing. That's one of the fun things - you never know what to expect - and that's quite all right! It's like trying to solve a puzzle. If it was that easy - it would take away that sense of Aha! when you succeed! I would definitely not try...

• Thanks @RosemarieMiddleton. Another tip is to keep your fingers steady and make sure you fix the flexagon in space so you don't get muddled up @InekeFioole

• I wouldn't go into the formality of the numbers after the T in the T-tuck flex. They relate to which vertex needs to be opened up, once choosing a vertex and starting the tuck. You can read more about it here: http://loki3.com/flex/explore/flex-compendium.html#T

• You are right. Template number 11 is, in fact, a hexaflexagon - I had intended it to be a triangle, but with all the templates running around I must have mixed them up... It does pyramid shuffle nicely through!

• Note that the tuck that you're doing here is not with a full tri-hexa-flexagon (the one with the pat structure 1-2-1-2-1-2. The hexa-hexa-flexagon supports nearly all the flexes this week but we'll get to that later on in the course.

• @SuzanneByrne I have - but you need to reload the webpage and clear the cache - otherwise your browser loads a "saved" version of the page with the old template...

• Because of daylight saving there's some confusion. @LeslyeSlater @JohnSloman
I originally meant:
19:00 in UK, 20:00 in Spain, 21:00 in Israel

but since there is some confusion I will stay online also at:
20:00 in UK, 21:00 in Spain, 22:00 in Israel

So people won't miss out...

• Yossi Elran replied to Paul C

Think of the faces of the flexagon - Going anticlockwise you go to the next pat - which is like going backwards i.e. the end of phrase

• Yossi Elran made a comment

It's time to see how you're doing and answer any questions you have on the course. Please join me for a Zoom Q & A session, Wednesday June 23rd at 19:00-19:30 UTC (which is 12:00 pm EDT and 21:00 IDT). Use this link:

https://weizmann.zoom.us/j/93337445368?pwd=SXduanQ3WmZmOVY3cEZBOWx2TlRCUT09

See you then!
Yossi

• Yossi Elran made a comment

It's time to see how you're doing and answer any questions you have on the course. Please join me for a Zoom Q & A session, Wednesday June 23rd at 19:00-19:30 UTC (which is 12:00 pm EDT and 21:00 IDT). Use this link:

https://weizmann.zoom.us/j/93337445368?pwd=SXduanQ3WmZmOVY3cEZBOWx2TlRCUT09

See you then!
Yossi

• Yossi Elran made a comment

It's time to see how you're doing and answer any questions you have on the course. Please join me for a Zoom Q & A session, Wednesday June 23rd at 19:00-19:30 UTC (which is 12:00 pm EDT and 21:00 IDT). Use this link:

https://weizmann.zoom.us/j/93337445368?pwd=SXduanQ3WmZmOVY3cEZBOWx2TlRCUT09

See you then!
Yossi

• Yossi Elran made a comment

It's time to see how you're doing and answer any questions you have on the course. Please join me for a Zoom Q & A session, Wednesday June 23rd at 19:00-19:30 UTC (which is 12:00 pm EDT and 21:00 IDT). Use this link:

https://weizmann.zoom.us/j/93337445368?pwd=SXduanQ3WmZmOVY3cEZBOWx2TlRCUT09

See you then!
Yossi

• Yes. You always tape at the end. This flexagon is for notation purposes only - just for examining - so you don't have to flex it. In fact, you haven't learned the specific flex that flexes it yet...

• Just reverse the moves... @JohnSloman

• OK @NanceyAlexa - I've redone the video - hope you can see better now :-)

• Are you OK with the taping now @InekeFioole ?

• Yes - you are of course correct - my mistake. I've corrected it now.

• @InekeFioole The error is in step 3.3 - I'll fix that. Using Scott's definition, there should be square brackets at the beginning and the end.

• Hi @InekeFioole - yes - pats can - and do - contain one leaf. Think of the tri-hexa-flexagon - its pats alternate 1-2-1-2-1-2.

• Yossi Elran replied to Paul C

Yes - you are of course correct - my mistake. I've corrected it now.

• Yes - you are of course correct - my mistake. I've corrected it now.

• Yes - the vertices are the points on the circumference of the polygons - where the edges meet.

• Glad to hear :-) You'll catch up quickly - don't worry - we've really spread out this course so that those who order the booklet will have time to do everything!

• Good for you - and her!

• Yossi Elran replied to Mark Booth

...and here is Scott's answer: For ^, you turn it over across the axis that goes through the current hinge. So, if the current hinge is at the top, you turn it over across the vertical axis

• Yossi Elran replied to Ben Weston

Maybe... :-) If you like you can video or photo it so we can see....

• Yossi Elran replied to Mark Booth

Absolutely true. I hadn't thought of that. I'll ask Scott what he intended it to mean.. :-)

• The only means that this is the only flex you can perform on the flexagon. It does not however refer to the number of times you can do this on a given flexagon, since sometimes this is not controllable. Yet, for the flip flex it is also true that this can only be done once.

• Yossi Elran replied to David Webb

Don't! Please! You'll get it... Just try and mimic the moves in the video using (a lot of) pause and play :-)

• Yes the online courses are still running but unfortunately not any more in English (these and hopefully more Future Learn courses have replaced them).

• Yes - very much so! This is the main reason that they are hidden.

• I'll definitely take that into account for the next runs... If I can I'll redo some of the videos again for this course...

• Wow! and so romantic... ;-)

• You did it great!

• Thanks @SueC - hope you feel better soon :-)

• Yossi Elran replied to Lyn Adams

I think this course will be open indefinitely but if not we will try and make other runs.

• Great solution! @JenniferBoag

• Thanks for spotting that - I corrected that! @ZoharBengad

• Just so you have spares - not to waste paper...

• Yes - just post the comment on your own page and tag it by writing #FLflexagonsgalore anywhere in the post

• See pinned comment above :-)

• One of the problems with Hilton and Pederson's naming system is that we can't know for sure what's the shape of the leaf. So all we can say is that the tetra-tetra has 4 faces and 4 identical shapes on each face, though these might be triangles, squares etc. Conventionally however, if nothing else is mentioned, they are assumed to be triangle. Of course,...

• You can mute the music if you find it annoying....
A word about “instructions” and “frustration”. There is no proper learning without frustration... the trial and error part of making and flexing flexagons is really important - and the only way you’ll really learn. When things get more difficult we’ve added some explanations in the text but you’ll get to that...

• Good luck to both of you!

• I think it should! I know it took 9 days to reach London and you really only need it from the third week on...

• Yossi Elran replied to V L

That’s even better! I’m sure you’ll learn better this way! @VL

• Hi @LornaAllen there are no transcripts - all that you need is written in the body of the text!

• Your right! Sorry about that! That should have definitely been found in quality analysis... You need to tape the top right-hand side wad of paper so you fold the tape from the front to the back of the top right-hand smiley face wad.

Now that I've reprimanded myself for doing such a bad job by obscuring the actual taping with my hand, I would however like...

• Yay!

• A4 works for all templates in this course.

• Yossi Elran replied to Anna Gann

Sorry about that. Most of the videos on the course do not have any talk - as part of what we learned from the first course and so that we can use the many videos we filmed for other language versions. Instead, we focused on the hand movements which are best viewed at 0.5 speed.

• Sorry but the volume hasn't been turned up so maybe your hearing got better :-) Most of the videos on the course do not have any talk - as part of what we learned from the first course and so that we can use the many videos we filmed for other language versions. Instead we focused on the hand movements which are best viewed at 0.5 speed.

• @ShirleyRawlings @GeraldJones @ChristaLloyd - You need to book flex all the way over. Sometimes the last flex is a bit tough but it will work with a bit of force. Make sure the tape is over the whole "smiley face" wad!

• Thanks so much! I hope you enjoy the course!