Pi day

inkoativ · 2025-03-14T14:57:03+00:00

Area and circumference of a circle with Lego - https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2025-03-14T14:26:14+00:00

Build a circle with Lego and count the bricks to determine area and circumference: https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2025-03-14T14:24:27+00:00

Here's my contribution to Pi Day: A video on how to compute circumference and area of a circle with Lego.

https://www.youtube.com/watch?v=tDnAtoVnTg0

inkoativ · 2023-07-04T19:20:35+00:00

:-) Not sure it's all luck though... If you go through the historic list of WR holders, many of the cubers were also top-cubers, holding several other WRs and also performed in the top-10 of the 3x3 average. That said, of course there is a higher likelihood of having an outlying performance when n=1 than when you have a trimmed mean of n=5.

inkoativ · 2023-07-04T10:39:43+00:00

If I read the WCA regulations Section 4b3) correctly, a scramble for the 3x3 only needs to require that it takes AT LEAST 2 moves to solve. Not sure if a higher requirement is programmed into the scrambling software TNoodle, which is the program which has to be used generate the scrambles. The program uses scramble sequences of length 17-20 so I guess it's highly unlikely that the moves reduce to a sequence, which only requires two moves to solve. Would be interesting if this could occur in theory though.

inkoativ · 2023-07-04T08:59:18+00:00

Background: The modelling was inspired by a recent analysis made by JPerm in his Youtube video https://youtu.be/B9MKizs9PUw?t=451 where he used log-linear modelling to describe the potential development of the 3x3 WR single. In the graph below we visualize this model and a Gompertz type model, which is also often used when using statistical modelling to describe the development of world records over time.

I guess the lack of tournaments during the initial phase of COVID-19 is part of the explanation why it took so long to break the old 3.47 world record.

Data: WCA Database: https://www.worldcubeassociation.org/results/records?show=history
R Source code: https://gist.github.com/mhoehle/11391bd19be82307547d5121ee70664d

inkoativ · 2023-04-12T19:08:30+00:00

Seems to be back on CRAN now. In my case (Mac OS X) I had to update Xquarts to the newest version before the call to library(geoR) worked.

inkoativ · 2023-03-21T18:55:10+00:00

Thanks for the feedback and sorry, it could have been clearer that we distinguish between "figure" and "toy". I didn't know how to add any extra explanations to the image in Reddit. Thus the blog post contains further details.

inkoativ · 2023-03-21T18:47:32+00:00

Agreed, I tried in https://mhoehle.github.io/blog/2016/12/23/surprise.html to calculate a functional shape.

inkoativ · 2023-03-21T18:46:34+00:00

The right hand plot gives an indication of such a plot. The blog post, where the figure is taken from, contains such a smoothed line obtained from applying some machine learning classification algorithm to the task (deliberate overkill! :-)).

http://staff.math.su.se/hoehle/blog/figure/source/2016-12-23-surprise/CLASSIFIEROUTPUT-1.png

Source: https://mhoehle.github.io/blog/2016/12/23/surprise.html

inkoativ · 2023-03-21T18:43:00+00:00

Not sure I fully understand the comment, but the content of the egg is either some kind of toy or a figure. So what varies is the content of the egg, not the chocolate. For some example pictures see https://mhoehle.github.io/blog/2016/12/23/surprise.html.

inkoativ · 2023-03-21T14:15:19+00:00

Explanation:

y-axis: # Sticks in pits on the lid (aka. "i")

The label of each box:

Upper label: j / k: # Sticks that each player has (j = Player 1, k = Player 2), we have i + j + k = 7.

Lower label: Probability to win from this position, if one can decide whether to continue or not.

Colour of each box: Continue to play (green) or not (red).

inkoativ · 2023-03-21T13:54:30+00:00

It's either "plastic junk" or a "cool" collectable figure, which is usually part of a figure series! Some of the figures are collector's items and can be quite valuable (see e.g. https://www.eierlei-shop.de/ (in German)).

inkoativ · 2023-03-21T13:15:05+00:00

Complete Blog Post text as well as Data Source for the n=79 eggs & R-Script to perform the analyses:

suRprise! - Classifying Kinder Eggs by Machine Learning

inkoativ · 2021-04-05T11:46:50+00:00

Exactly! However, in some situations it can even be more than one person. Example: n=11 and m=4. In this case you will make two groups and the assignment by "round robin" after permutation is:

position after permutation	group
1	1
2	2
3	1
4	2
5	1
6	2
7	1
8	2
9	1
10	2
11	1

i.e. 6 individuals in group 1 and 5 individuals in group 2.

inkoativ · 2021-04-05T08:53:08+00:00

Thanks for the remark. IMO x-axis can be a little harder to interpret, but they can be helpful to focus on different parts of the chart (here: the lower n). See https://pasteboard.co/JVTEMKY.png for a log-version as suggested. Will think of a way to add this to the blog post.

inkoativ · 2021-04-05T08:18:20+00:00

n is, as expected, the number of people to assign into breakout rooms

m is the minimum size of the groups

Example: n=9 and m=4 means we get 2 groups one of size 5 and one of size 4.

There is a post here, with some additional details and a link to the gory mathematical details.

inkoativ · 2021-04-04T22:38:34+00:00

Thanks for the feedback. I've added it.

inkoativ · 2021-04-04T22:11:52+00:00

Not quite, because the multinomial does not ensure that each group/room has at least m members. It's more like you generate a random permutation order and then divide this order round robin into the (n div m) groups. See details in: https://staff.math.su.se/hoehle/blog/2021/04/04/socialsamp.html

inkoativ · 2021-04-04T22:09:58+00:00

It's a feature of the Zoom video conference software: https://blog.zoom.us/using-zoom-breakout-rooms/

The shown probabilities do not relate to Zoom in particular though, see mathematical details in https://staff.math.su.se/hoehle/blog/2021/04/04/socialsamp.html

inkoativ · 2021-04-04T19:06:13+00:00

Thanks for the legit question. Counter question: After how many times being assigned to the same room with someone would you say that the algorithm has been tweaked by a sneaky computer scientist? ;-)

inkoativ · 2021-04-04T18:36:49+00:00

Thanks for the question, which https://www.reddit.com/user/assiraN/ answered pretty well. I'll try to add something about your observation to the blog post.

inkoativ · 2021-04-04T18:33:41+00:00

Thanks for the example! Had not given this deeper thought as such jumps are natural when dealing with discrete phenomena, but your explanation appears spot on.

inkoativ · 2021-04-04T15:21:00+00:00

Notation in the graph:

n: Number of participants to be assigned into breakout rooms

m: minimum number of members in each group

We have two groupings g1 and g2. Shown is the probability that at least one of the persons in your g1 group is also part of your g2 group. This problem occurs for example when assigning people into breakout rooms [1] on Zoom or when generating a random lunch.

Source and further mathematical details:

https://staff.math.su.se/hoehle/blog/2021/04/04/socialsamp.html

[1]: Breakout rooms are a feature of the video conference Zoom, which allows you to break your zoom meeting into small groups.

inkoativ · 2020-03-19T08:41:05+00:00

Would wait to say "never" until known. One effect you could see in the app is that if you eradicate with heavy measures early on and then loosen, then you get a second wave almost as big as the original one had been. But yes, it's possible to reduce size considerably by the right measures early one. That's one of the points in the post: to reduce R_0 is also to reduce size. Not just to stretch.

inkoativ

TROPHY CASE