Eric Lengyel
@ericlengyel.bsky.social
• Creator of Radical Pie equation editor, Slug Library, C4 Engine
• Math / gamedev author
• Geometric algebra researcher
• Former Naughty Dog, Apple, Sierra
• Math / gamedev author
• Geometric algebra researcher
• Former Naughty Dog, Apple, Sierra
When a is a vector and b is any multivector, the geometric product a ⟑ b decomposes as
a ⟑ b = a ∧ b + b ∨ (a^★),
and b ⟑ a decomposes as
b ⟑ a = b ∧ a + (a_★) ∨ b.
If a and b are both vectors, these both reduce to
a ⟑ b = a ∧ b + a ⋅ b.
a ⟑ b = a ∧ b + b ∨ (a^★),
and b ⟑ a decomposes as
b ⟑ a = b ∧ a + (a_★) ∨ b.
If a and b are both vectors, these both reduce to
a ⟑ b = a ∧ b + a ⋅ b.
February 6, 2026 at 10:41 PM
When a is a vector and b is any multivector, the geometric product a ⟑ b decomposes as
a ⟑ b = a ∧ b + b ∨ (a^★),
and b ⟑ a decomposes as
b ⟑ a = b ∧ a + (a_★) ∨ b.
If a and b are both vectors, these both reduce to
a ⟑ b = a ∧ b + a ⋅ b.
a ⟑ b = a ∧ b + b ∨ (a^★),
and b ⟑ a decomposes as
b ⟑ a = b ∧ a + (a_★) ∨ b.
If a and b are both vectors, these both reduce to
a ⟑ b = a ∧ b + a ⋅ b.
Whoa, the SIGGRAPH exhibit floor is tiny this year. This used to be a huge show! What the heck is going on?
maps.goeshow.com/acm/siggraph...
maps.goeshow.com/acm/siggraph...
January 29, 2026 at 11:02 PM
Whoa, the SIGGRAPH exhibit floor is tiny this year. This used to be a huge show! What the heck is going on?
maps.goeshow.com/acm/siggraph...
maps.goeshow.com/acm/siggraph...
This might be the first year since 1999 that I don't attend GDC.
January 29, 2026 at 5:17 AM
This might be the first year since 1999 that I don't attend GDC.
This is a reminder that every diagram from my book Projective Geometric Algebra Illuminated is available on Wikimedia Commons under the CC-BY-4.0 license. They can be freely used in slides, papers, books, Wikipedia articles, etc., with proper attribution.
commons.wikimedia.org/wiki/User:Er...
commons.wikimedia.org/wiki/User:Er...
January 27, 2026 at 2:36 AM
This is a reminder that every diagram from my book Projective Geometric Algebra Illuminated is available on Wikimedia Commons under the CC-BY-4.0 license. They can be freely used in slides, papers, books, Wikipedia articles, etc., with proper attribution.
commons.wikimedia.org/wiki/User:Er...
commons.wikimedia.org/wiki/User:Er...
Reposted by Eric Lengyel
Lengyel's conventions. Fuck yeah.
I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism. The results of my efforts are now being adopted by prominent scientists and engineers in various fields.
January 23, 2026 at 9:31 PM
Lengyel's conventions. Fuck yeah.
I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism. The results of my efforts are now being adopted by prominent scientists and engineers in various fields.
January 23, 2026 at 9:21 PM
I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism. The results of my efforts are now being adopted by prominent scientists and engineers in various fields.
John Christian's new book Fundamentals of Spacecraft Optical Navigation arrived today.
January 23, 2026 at 12:50 AM
John Christian's new book Fundamentals of Spacecraft Optical Navigation arrived today.
I added LaTeX output to the latest version of Radical Pie, which was released today. It can't handle everything that Radical Pie can do, but it tries its best to faithfully reproduce equations that can be written in basic LaTeX code without requiring obscure packages.
January 19, 2026 at 10:37 PM
I added LaTeX output to the latest version of Radical Pie, which was released today. It can't handle everything that Radical Pie can do, but it tries its best to faithfully reproduce equations that can be written in basic LaTeX code without requiring obscure packages.
FGED3 adds five new chapters to the series:
11 • Curves
12 • Motion Operators
13 • Models and Animation
14 • Advanced Shading
15 • Special Effects
I'm shooting for a SIGGRAPH 2026 release.
(The cover is not necessarily final.)
11 • Curves
12 • Motion Operators
13 • Models and Animation
14 • Advanced Shading
15 • Special Effects
I'm shooting for a SIGGRAPH 2026 release.
(The cover is not necessarily final.)
January 18, 2026 at 10:38 PM
FGED3 adds five new chapters to the series:
11 • Curves
12 • Motion Operators
13 • Models and Animation
14 • Advanced Shading
15 • Special Effects
I'm shooting for a SIGGRAPH 2026 release.
(The cover is not necessarily final.)
11 • Curves
12 • Motion Operators
13 • Models and Animation
14 • Advanced Shading
15 • Special Effects
I'm shooting for a SIGGRAPH 2026 release.
(The cover is not necessarily final.)
Some things I learned when talking to people at JMM this week:
• Most find the Radical Pie UI to be very intuitive.
• A Mac version would be useful even if it doesn't integrate with Word as it does on Windows.
• Nobody likes the Microsoft Office equation editor. And I mean nobody.
• Most find the Radical Pie UI to be very intuitive.
• A Mac version would be useful even if it doesn't integrate with Word as it does on Windows.
• Nobody likes the Microsoft Office equation editor. And I mean nobody.
January 9, 2026 at 7:52 PM
Some things I learned when talking to people at JMM this week:
• Most find the Radical Pie UI to be very intuitive.
• A Mac version would be useful even if it doesn't integrate with Word as it does on Windows.
• Nobody likes the Microsoft Office equation editor. And I mean nobody.
• Most find the Radical Pie UI to be very intuitive.
• A Mac version would be useful even if it doesn't integrate with Word as it does on Windows.
• Nobody likes the Microsoft Office equation editor. And I mean nobody.
I’ve been getting a lot of great reactions from people discovering Radical Pie at the Joint Mathematics Meetings this week.
January 6, 2026 at 4:23 PM
I’ve been getting a lot of great reactions from people discovering Radical Pie at the Joint Mathematics Meetings this week.
I’m in Washington DC for the Joint Mathematics Meetings. The exhibits open tomorrow, and Radical Pie is right up front.
January 3, 2026 at 8:03 PM
I’m in Washington DC for the Joint Mathematics Meetings. The exhibits open tomorrow, and Radical Pie is right up front.
Tomorrow, I leave for Washington DC where I'll be showing the brand new Radical Pie equation editor at the Joint Mathematics Meetings conference. If you're attending, come check it out at booth #505. I'm also going to have plenty of materials about projective geometric algebra.
January 1, 2026 at 11:26 AM
Tomorrow, I leave for Washington DC where I'll be showing the brand new Radical Pie equation editor at the Joint Mathematics Meetings conference. If you're attending, come check it out at booth #505. I'm also going to have plenty of materials about projective geometric algebra.
Version 1.2 of the Radical Pie equation editor has been released. This version contains some new features and a couple minor bug fixes. This is a free upgrade for all users.
radicalpie.com
radicalpie.com
January 1, 2026 at 1:23 AM
Version 1.2 of the Radical Pie equation editor has been released. This version contains some new features and a couple minor bug fixes. This is a free upgrade for all users.
radicalpie.com
radicalpie.com
Slug version 7.5 has been released. This update includes several small feature improvements.
sluglibrary.com
sluglibrary.com
December 31, 2025 at 7:31 AM
Slug version 7.5 has been released. This update includes several small feature improvements.
sluglibrary.com
sluglibrary.com
Reposted by Eric Lengyel
The MathPad 1A mini keyboard from @summacogni.bsky.social works spectacularly for #emacs org-mode, LaTeX in Markdown and surprisingly also with the #radicalpie equation editor from @ericlengyel.bsky.social out of the box
I'd maybe change the sub & super-script indices that insert unicode not boxes.
I'd maybe change the sub & super-script indices that insert unicode not boxes.
December 20, 2025 at 3:48 AM
The MathPad 1A mini keyboard from @summacogni.bsky.social works spectacularly for #emacs org-mode, LaTeX in Markdown and surprisingly also with the #radicalpie equation editor from @ericlengyel.bsky.social out of the box
I'd maybe change the sub & super-script indices that insert unicode not boxes.
I'd maybe change the sub & super-script indices that insert unicode not boxes.
For the upcoming JMM conference, I've got FGED1, FGED2, PGA Illuminated, the OpenGEX specification, my Master's Thesis, Dissertation, and a bunch of papers all remastered with Radical Pie for a total of 13,157 equations. I'd say it's sufficiently tested.
December 17, 2025 at 6:41 AM
For the upcoming JMM conference, I've got FGED1, FGED2, PGA Illuminated, the OpenGEX specification, my Master's Thesis, Dissertation, and a bunch of papers all remastered with Radical Pie for a total of 13,157 equations. I'd say it's sufficiently tested.
I built a new shipping crate in my garage that I'll be using to send stuff to trade shows. It's on its way to Washington DC now for the Joint Mathematics Meetings in early January, where I'm introducing the Radical Pie equation editor.
December 14, 2025 at 11:50 PM
I built a new shipping crate in my garage that I'll be using to send stuff to trade shows. It's on its way to Washington DC now for the Joint Mathematics Meetings in early January, where I'm introducing the Radical Pie equation editor.
Reposted by Eric Lengyel
December 13, 2025 at 4:59 AM
Radical Pie is the official lanyard sponsor of the Joint Mathematics Meetings 2026. This is the largest mathematics conference in the U.S. and a perfect place for the Radical Pie equation editor to make its academic debut.
December 8, 2025 at 8:36 PM
Radical Pie is the official lanyard sponsor of the Joint Mathematics Meetings 2026. This is the largest mathematics conference in the U.S. and a perfect place for the Radical Pie equation editor to make its academic debut.
Visual Studio 2026 has a new "Generate preprocessed output for any C++ file" feature that brings us one step closer to parity with the development functionality available in 1995 with CodeWarrior.
November 21, 2025 at 7:16 AM
Visual Studio 2026 has a new "Generate preprocessed output for any C++ file" feature that brings us one step closer to parity with the development functionality available in 1995 with CodeWarrior.
Version 1.1 of the Radical Pie equation editor has been released. This is a free upgrade for all users.
radicalpie.com
radicalpie.com
November 20, 2025 at 2:17 AM
Version 1.1 of the Radical Pie equation editor has been released. This is a free upgrade for all users.
radicalpie.com
radicalpie.com
Projective Geometric Algebra Illuminated has also been remastered with the Radical Pie equation editor in both the soft and hard cover formats. The content is the same, but all 4919 equations appearing in the text plus every equation in every figure has been upgraded with RP.
November 18, 2025 at 10:57 PM
Projective Geometric Algebra Illuminated has also been remastered with the Radical Pie equation editor in both the soft and hard cover formats. The content is the same, but all 4919 equations appearing in the text plus every equation in every figure has been upgraded with RP.
FGED 1&2 have been remastered with the Radical Pie equation editor, and the new versions are now available on Amazon (links below). The content is exactly the same, but the mathematical typesetting got an upgrade. The remaster applies to the soft cover versions only.
November 18, 2025 at 10:47 PM
FGED 1&2 have been remastered with the Radical Pie equation editor, and the new versions are now available on Amazon (links below). The content is exactly the same, but the mathematical typesetting got an upgrade. The remaster applies to the soft cover versions only.
Writing documentation and watching game 7 of the World Series tonight.
November 2, 2025 at 2:07 AM
Writing documentation and watching game 7 of the World Series tonight.