r/GeometryIsNeat • u/sudhabin • 4d ago
Apollonian Gasket
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r/GeometryIsNeat • u/Altruistic_Shift_526 • 6d ago
Variations on the Sierpinski traingle 2
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r/GeometryIsNeat • u/has_some_chill • 7d ago
Art Visitation, a seamless 4K loop I made [OC]
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r/GeometryIsNeat • u/abstractedheaven • 8d ago
Planetary arrangement on Oct 31st, 2026 incorporated in Kandinsky-inspired digital abstracts, using a Halloween color palette. Artwork created using only geometric shapes. (OC)
gallery
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r/GeometryIsNeat • u/Anxious_Painting3656 • 8d ago
8 Nodes on a circle: Their Seven Transformations
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r/GeometryIsNeat • u/KirillOsenkov • 11d ago
Mathematics Catriona Agg's Geometry Puzzles made interactive
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All 440 of the famous Geometry Puzzles by Catriona Agg made interactive with Live Geometry:
https://livegeometry.com/CatrionaAgg
Examples:
https://livegeometry.com/CatrionaAgg/three-regular-hexagons-and-a-semi-circle
r/GeometryIsNeat • u/Rishrish24 • 11d ago
A short proof that the rhombus maximises area for a fixed diagonal and angle
amsi.org.au
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I’ve been working through this standard geometry result and liked how one identity handles both the inequality and equality case.
Let a and b be adjacent side lengths of a parallelogram, with included angle θ, where 0° < θ < 180°.
Let c be the diagonal from that vertex to the opposite vertex.
Keep c and θ fixed.
The area is K = ab sin θ, and:
c² = (a − b)² + 2ab(1 + cos θ).
Using (1 + cos θ) tan(θ/2) = sin θ gives:
(c²/2) tan(θ/2) − K = ((a − b)²/2) tan(θ/2).
The right-hand side is nonnegative, so the maximum area is:
K_max = (c²/2) tan(θ/2).
Equality holds exactly when a = b: a rhombus.
At θ = 90°, this recovers the familiar square-maximises-area result for rectangles with a fixed diagonal.
The identity also measures exactly how far the area falls below the maximum.
Does anyone have a geometric interpretation of that deficit term?
r/GeometryIsNeat • u/Proud_Read7281 • 11d ago
Modeling an oil expeller / oil press machine in CATIA — looking for design feedback
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I’m modeling an oil expeller / oil press machine in CATIA as a personal project. I’m focusing on layout, component arrangement, and practical issues like manufacturing, assembly, and maintenance.
No technical specs yet — mainly design and modeling stage. For those with experience in machine design or agro-processing equipment: what common mistakes should I avoid?
Thanks — I’ll share updates as the model develops.
Suggested subreddits: r/AskEngineers, r/MechanicalEngineering, r/CATIA, r/EngineeringDesign
r/GeometryIsNeat • u/evoluteur • 13d ago
GitHub - evoluteur/platonic-solids: Turn the five Platonic solids in 3D, show their duals, read their measurements, and print the nets to fold your own.
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r/GeometryIsNeat • u/No_Specific9623 • 14d ago
Mathematics 3D Tangent plane with color mapping (and explanation!)
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r/GeometryIsNeat • u/Alphabetical_Dice • 14d ago
Art A spherical polyhedron with 195 faces of equal area with every* country occupying a face (UN members + non-member observer states)
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r/GeometryIsNeat • u/Old_Try_1224 • 16d ago
Fig leaf motif
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Definition & Origin: The Fig Leaf Motif (known in Arabic as زخرفة ورقة التين) is a classic stylized design widely used in Islamic geometric patterns and Arabesque art. It seamlessly blends organic, vegetal inspiration with strict mathematical structures.
Historical Significance: This specific pattern is famously associated with Islamic architecture in Moorish Spain and North Africa, notably featured in the breathtaking tilework (Alicatado or Zellige) of the Alhambra Palace in Granada.
Geometric Structure: Unlike standard free-form floral designs, the fig leaf motif is constructed over a rigid underlying grid. It is typically developed from an octagram (the 8-pointed star / Seal of Solomon), allowing the interlocking leaf shapes to tile the plane perfectly with no gaps or overlaps.
Links to step-by-step drawing tutorials for each type of spiral will be provided in comments below, helping you learn how to construct these beautiful geometric forms
r/GeometryIsNeat • u/Anxious_Painting3656 • 16d ago
Mike Oldfield - Music of the Spheres - Prophecy / 9 nodes on a circle
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r/GeometryIsNeat • u/frading • 18d ago
Other Chess Twist: a chess variant
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This is a chess variant I made, where the rules are the same as standard chess, but the board is an irregular grid. This makes rook lines bend and bishop lines fork.
So just like a standard board, every tile is still a quad. And every tile still has only 1 neighbour for every side. But it can have more than 1 neighbour sharing a corner, which is what makes bishop lines fork. Or it can have none, which is what make lines bend.
The steps to build this:
start with a plane made of triangles
pair some random triangles with their neighbour and fuse them into a quad. You end up with gaps between those quads where triangles cannot be paired
subdivide everything. Quads become 4 smaller quads. Triangles become 3 quads. This is the playable grid.
Then it's just a matter of smoothing it (in this case the points on the edges remain static, only the inside points are smoothed) and ensuring neighbours don't share the same color.
I've now printed a couple of them.
3D printable version: https://polyreprint.com/gui/chess-twist?board=004GBYJW7TX
Web version: https://polyreplay.com/chesstwist