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Michael Borcherds

@mikegeogebra

CTO | GeoGebra #edtech #geogebra #pyggb #webusb

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12.06.2023
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Latest posts by Michael Borcherds @mikegeogebra

Barney Maunder-Taylor says a square-based pyramid is exactly twice the volume of a triangular-based one (same side length). He doesn't want the tedious trig approach to proving it though, he wants a more intuitive route. He'll try the usual proof by @geogebra.org instead #mathsjam

23.11.2025 13:45 ๐Ÿ‘ 3 ๐Ÿ” 3 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Welcome to AMiE
Welcome to AMiE YouTube video by Association for Mathematics in Education (AMiE)

๐Ÿ“ฃ Weโ€™re excited to welcome you to the newly formed Association for Mathematics in Education!

After bringing together five long-standing associations, weโ€™re proud to unite our communities, expertise, and energy under our new association.

Watch our welcome video: www.youtube.com/watch?v=1uLL...

01.12.2025 12:33 ๐Ÿ‘ 11 ๐Ÿ” 10 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Weโ€™re looking forward to seeing everyone at MathsJam Gathering this weekend - follow along here to see what people are sharing, and use #mathsjam to share your favourite moments!

18.11.2025 12:23 ๐Ÿ‘ 2 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

After some confusing back and forth interactions, I've realized that "I moved the meeting back by 30 min" is interpretable as both:
- "moved earlier by 30 min", and
- "moved later by 30 min"

03.11.2025 20:47 ๐Ÿ‘ 8 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0

Works nicely, very cool ๐Ÿ™๐Ÿ™๐Ÿ™

28.10.2025 10:40 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Preview
Third of a cube (assemblable, with clearance) - Download Free 3D model by robinhouston This is exported from BurrTools with the following parameters: Unit size: 10.00 Bevel: 0.30 Offset: 0.1 Wall Thickness: 0.00 Tubes size: 0.05 Leave inside grooves: no Leave outside grooved: no Remove grooves in void: no - Third of a cube (assemblable, with clearance) - Download Free 3D model by robinhouston

If anyone wants to try printing this and testing it in the real world, the model here might be more suitable: it has slightly rounded edges, and the faces are slightly inset to give more clearance when assembling it. https://skfb.ly/pzDKY

29.07.2025 16:34 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
Preview
Five Fit - Tray-packing puzzle by Stewart Coffin (STC #177-A) by asiegel Five FitTray-packing puzzle by Stewart Coffin (STC #177-A)Fit all five pieces into the square opening.Five Woods is one of a series of tray-packing puzzles by Stewart Coffin. It seems impossible at fi...

Did you solve it? Looks interesting!

This one is very good, also by Stuart Coffin www.thingiverse.com/thing:3433358

27.10.2025 11:40 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
A photograph of a tray-packing puzzle, showing a tray containing three pentominos with a fourth pentomino separately. The puzzle is to fit all four into the tray.

A photograph of a tray-packing puzzle, showing a tray containing three pentominos with a fourth pentomino separately. The puzzle is to fit all four into the tray.

I spent hours yesterday (on a long plane journey) failing to solve Stewart Coffin's Four Fit puzzle. I tried everything I could think of, and nothing worked.

If you know the solution please don't tell me.

10.08.2025 15:15 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 4 ๐Ÿ“Œ 0
Original post on mathstodon.xyz

// Here is some OpenSCAD code, if you want to understand how I made it, or to make your own:

r = 10;
h = 60;

module hex_prism(i) {
rotate([acos(1/sqrt(3)), 0, i * 90])
linear_extrude(height = h, center=true)
circle(r, $fn=6);
}

for(i=[0 : 1 : 3])
for(j=[i + 1 : 1 : 3])
for(k=[j + 1 : 1 : 3]) [โ€ฆ]

14.10.2025 22:24 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
A pile of small white plastic pieces, tetrahedral with protruding pegs and holes so they can be joined to each other

A pile of small white plastic pieces, tetrahedral with protruding pegs and holes so they can be joined to each other

The first prototype came out better than I expected, though there's a lot of room for improvement still.

19.10.2025 10:36 ๐Ÿ‘ 1 ๐Ÿ” 1 ๐Ÿ’ฌ 2 ๐Ÿ“Œ 1

Thanks, it prints really nicely without supports ๐Ÿ˜ฎ๐Ÿ˜ฎ๐Ÿ˜ฎ
(on P1S)

27.10.2025 11:09 ๐Ÿ‘ 1 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Close up of side of turquoise noperthedron on a table. The shape is turquoise with triangulation where the band around it Center has smaller triangles and the top and bottom have longer triangles creating a belt around it that is more bulbus.

Close up of side of turquoise noperthedron on a table. The shape is turquoise with triangulation where the band around it Center has smaller triangles and the top and bottom have longer triangles creating a belt around it that is more bulbus.

A turquoise 3d printed  bulbous triangulated vase on a table with some rocks and weaving.

A turquoise 3d printed bulbous triangulated vase on a table with some rocks and weaving.

A noperthedron container printed!

#mathart #mtbos #noperthedron #polyhedra

30.08.2025 02:47 ๐Ÿ‘ 51 ๐Ÿ” 8 ๐Ÿ’ฌ 3 ๐Ÿ“Œ 4

Link is 404 for me ๐Ÿ˜ญ

25.10.2025 07:14 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
A teal noperthedron with a cylindrical hole in a drafting program with shadowing. The shape is vase-like with triangulated faces, but bulbous at the center and slanted inward at the top in bottom so that there is a band of 3 layers of shorter triangles in the middle and longer more angled-in triangles at the top and base of the vase (container).

A teal noperthedron with a cylindrical hole in a drafting program with shadowing. The shape is vase-like with triangulated faces, but bulbous at the center and slanted inward at the top in bottom so that there is a band of 3 layers of shorter triangles in the middle and longer more angled-in triangles at the top and base of the vase (container).

I am printing a noperthedron pencil holder :)

#mtbos #mathart #noperthedron

29.08.2025 20:28 ๐Ÿ‘ 87 ๐Ÿ” 14 ๐Ÿ’ฌ 3 ๐Ÿ“Œ 1
Video thumbnail

Patrons de pyramides "coupรฉes" par un plan.

#geogebra : www.geogebra.org/m/kjmjkmkj

#math #pyramid #net #geometry #patron

06.04.2025 10:08 ๐Ÿ‘ 4 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 1
Un rouleau de papier toilette incroyablement modรฉlisรฉ dans Geogebra.

Un rouleau de papier toilette incroyablement modรฉlisรฉ dans Geogebra.

- Tu sais utiliser Geogebra ?
- Oui, bien sur. Je l'utilise tout le temps pour rรฉaliser des figures de gรฉomรฉtrie un peu difficiles.

Mon utilisation rรฉelle de Geogebra :

12.09.2025 20:28 ๐Ÿ‘ 25 ๐Ÿ” 2 ๐Ÿ’ฌ 2 ๐Ÿ“Œ 0

Yes to everything that has already been mentioned. Additionally, I use some geogebra constructions as well (especially for linear optics, nice interactive demos for images from lenses, and multi-sense-systems)

16.09.2025 22:09 ๐Ÿ‘ 1 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
Video thumbnail

La Esfenocorona es un poliedro convexo con 12 โ–ณ equil. y 2 โ–ก, 22 aristas y 10 vรฉrtices. De estos, en 2 inciden 2 โ–ณ y 2 โ–ก, en ese orden; en 4 inciden 3 โ–ณ y un โ–ก; en los 4 restantes 5 โ–ณ. Es el sรณlido de Johnson J86.
#GeoGebra
ilarrosa.github.io/GeoGebra/Esf...
ilarrosa.github.io/GeoGebra

12.10.2025 23:05 ๐Ÿ‘ 2 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

Oh, also peterkagey.com/assets/blog/... is 404

13.10.2025 10:48 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0

Thanks so much ๐Ÿ™๐Ÿ™๐Ÿ™

Please check, piece 7 seems to be 404 peterkagey.com/assets/blog/...

13.10.2025 10:45 ๐Ÿ‘ 0 ๐Ÿ” 0 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
Preview
Pentagonal icositetrahedron puzzle A puzzle on the faces of the pentagonal icositetrahedron with 3D models, STL files, photos, and video illustrations

Sure thing! I wrote a blog post just for you which includes links to the STL files.

06.10.2025 01:34 ๐Ÿ‘ 2 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0

In-person tickets are selling fast for the MathsJam UK Gathering - join us (in-person or remotely!) for a weekend of recreational maths in a conference centre and meet others who also love maths! Details at www.mathsjam.com/gat...

02.10.2025 11:43 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

As well as our monthly pub meetings, there are also bigger annual MathsJam gatherings - one in the UK around November, and one in Oceania (New Zealand) - for details visit https://mathsjam.com/gathering

05.10.2025 15:01 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Video thumbnail

Tomorrow in Cal: The amazing e^x whose derivative is e^x. @geogebra makes these visuals so easy.

04.03.2021 03:10 ๐Ÿ‘ 0 ๐Ÿ” 1 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0

I've been seeing ads for the Shashibo toy. It looked like a more elaborate version of the kaleidocycle, which is fun to make out of paper. Shashibo is a ring of pyramids that comes in the shape of a cube but can be rearranged into a variety of shapes....

18.11.2022 21:31 ๐Ÿ‘ 2 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
The 'net' of a Polyhedron as a Stereographic Projections - TMIP Animation Challenge
The 'net' of a Polyhedron as a Stereographic Projections - TMIP Animation Challenge YouTube video by Ben Cornish

Hello @tmip.bsky.social et al.

Let me introduce my submission for the April Animation prompt of a 'Polyhedral Net'. I went with the type used for fishing, I hope you enjoy it.

#geogebra #mathanimations #mathsky #mathsanimationtmip

youtu.be/fCtsAXOo4NU

07.04.2025 11:55 ๐Ÿ‘ 5 ๐Ÿ” 3 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Post image

#PythonGgb : courbe de Gosper, un poil plus alambiquรฉe que la ligne de Hilbert...
Dรฉfi personnel, mais peu de plus value didactique par rapport aux usages sรฉparรฉs de #python et de @geogebra.
En classe, moins de spectaculaire, mais plus de gรฉomรฉtrie dynamique !
geogebra.org/python/index...

07.12.2023 17:14 ๐Ÿ‘ 3 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Post image Post image Post image Post image

I made this @geogebra applet that lets you play with Johan Gielis's polar super-formula. You can use it to make interesting shapes like these. https://www.geogebra.org/m/pprqzpja

21.08.2019 18:38 ๐Ÿ‘ 1 ๐Ÿ” 1 ๐Ÿ’ฌ 1 ๐Ÿ“Œ 0
ยฟHasta dรณnde podemos llegar con GeoGebra?

ยฟHasta dรณnde podemos llegar con GeoGebra?

Xa podemos empezar a desvelar cousiรฑas... <<ยฟHasta dรณnde podemos llegar con GeoGebra?>> รฉ o tรญtulo da ponencia coa que nos vai deleitar @bancoche.bsky.social no IV Dรญa GeoGebra de Galicia.
#ourense #15febreiro #diageogebragalicia @geogebra.org

03.01.2025 18:24 ๐Ÿ‘ 5 ๐Ÿ” 8 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0
Post image

Klein Bottle exploration in #GeoGebra #3d calculator with AR: youtube.com/shorts/NDXlX...

23.04.2025 19:01 ๐Ÿ‘ 4 ๐Ÿ” 2 ๐Ÿ’ฌ 0 ๐Ÿ“Œ 0