Basic Geometry · Jun 26, 2026 · 7:15 PM UTC

Basic Geometry

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Basic Geometry@BasicGeometryJun 26

The mathematical constant named pi is an artifact of a fundamentally flawed theoretical approximate. So are some other currently widely conventionally propagated formulas commonly referred to as Euclidean or specifically Archimedian. The CGS™ restores constructive geometry.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT 3.2radius² is the exact area of a circle. With proof.

ALT The mathematical constant named pi is an artifact of a fundamentally flawed theoretical approximate.

ALT Measuring the volume of a ball via liquid displacement.

Gaál Sándor@gmac4247Jun 26

True computational efficacy using the Core Geometric System™. - 3.2radius² is the exact area of a circle. From that: - 3.2diameter is its exact circumference. - (√3.2r)³ is the exact volume of a sphere. - Base × height / √8 is the exact volume of a cone or pyramid. #cgs

ALT 3.2radius² is the exact area of a circle.

ALT (√(3.2)r)³ is the exact volume of a sphere.

ALT Base × height / √8 is the exact volume of a cone.

ALT Base × height / √8 is the exact volume of a cone or pyramid.

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Basic Geometry · Oct 27, 2026 · 9:05 AM UTC

Basic Geometry@BasicGeometryOct 27

That is a crucial clarification.

Gaál Sándor@gmac4247Oct 27

Replying to @gmac4247

So, what the mathematical constant pi really stands for is the expression n×sin(180°/n)<pi<n×tan(180°/n). With n approaching infinity, that is 3.14... But that is not the true circumference to diameter ratio; it's just a failed approximate of it. ... nitter.gq/BasicGeometry/status/2…

ALT Pi approximation

Gaál Sándor · Oct 27, 2026 · 7:14 AM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Oct 27

I have to set the record straight regarding an important detail. It doesn't fit into a single post, so it will be a short thread. It's a recurring issue, that some claim that I claim "pi=3.2". That is false. It's the same with the Indiana Pi Bill. ...

Gaál Sándor@gmac4247Sep 5

3.2radius² is the exact area of a circle. From that 3.2diameter is the exact circumference. Confirmed via measurements. The wise insist that can't be, because their theoretical circumscribed polygon limits it to about 3.14. Their polygon is not as circumscribed as they think.

ALT 3.2radius² is the exact area of a circle.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT Arc and tangent line

ALT Arc and tangent line spacing

Basic Geometry · Oct 26, 2026 · 5:31 AM UTC

Basic Geometry@BasicGeometryOct 26

Replying to @ZebMic @justinskycak

Remember the mathematical constant named pi? They claim to "prove" it via calculus. Measure the circumference to diameter ratio of a coin, then think about that. Their conventional sphere volume formula is about one third off, but they "prove" it via calculus.

ALT 3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle. With proof.

ALT Circle and square area comparison.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

Basic Geometry · Oct 25, 2026 · 8:18 PM UTC

Basic Geometry@BasicGeometryOct 25

Replying to @chujusansuu

This is why you should never use pi=3.14... The area of a circle equals the area of a concentric square only if the arc divides the sides into 4 equal parts. That makes the side to radius ratio 4 / √5.

ALT 3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle. With proof.

ALT Circle and square area comparison.

407

Gaál Sándor · Oct 25, 2026 · 7:55 PM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Oct 25

Don't fall for this type of fraud. The true volume of a sphere equals the cubic value of the square root of its cross-sectional area — just like a cube —, which is about a third larger than the result of this worthless, primitive, exaggerated approximate. Measure it.

Mathematica

@mathemeticaOct 24

The sphere’s true volume is revealed by what remains after the cones are removed. Every horizontal slice of the sphere is a disk of radius √(r² − z²). The cylinder with its double cone subtracted leaves an annulus of outer radius r and inner radius |z|. Both areas equal π(r² − z²). Cavalieri’s principle therefore equates the volumes. Subtract the two cones from the cylinder: 2πr³ − 2·(⅓πr³) = ⁴⁄₃πr³. The sphere occupies exactly two-thirds of its enclosing cylinder. Geometry finds equality in the slices we choose to compare.

Basic Geometry · Oct 22, 2026 · 5:17 PM UTC

Basic Geometry@BasicGeometryOct 22

Replying to @miniapeur

Allegedly, that person turned basic geometry into the mess it is today. Everything built on that is messed up — including "real" analysis and physics. It's not just about difficulty; it's about deviant philosophy presented as "real" science.

Basic Geometry · Oct 11, 2026 · 9:24 AM UTC

Basic Geometry@BasicGeometryOct 11

Replying to @BasicGeometry @miniapeur

Verifying that it's an identity; not tautology: Note, that the arc intersects the sides exactly at their quarters only if side / radius = 4 / √5.

ALT Circle and square area comparison

Basic Geometry · Oct 7, 2026 · 6:46 AM UTC

Basic Geometry@BasicGeometryOct 7

The arc intersects the sides of a concentric square at its quarters only if side/radius=4/√5, hence 3.2r² is the only true area balance ratio.

ALT Circle area diagram

ALT Constructive algebraic proof of 3.2radius² is the exact area of a circle 1/3

ALT Constructive algebraic proof of 3.2radius² is the exact area of a circle 2/3

ALT Constructive algebraic proof of 3.2radius² is the exact area of a circle 3/3

Gaál Sándor@gmac4247Sep 2

"Debunked..." My ass. It's much more like I have debunked the academic community as a bunch of degenerate liers and fraudsters. You just need to pull your heads out of their butts to see it.

Basic Geometry · Oct 3, 2026 · 3:49 PM UTC

Basic Geometry@BasicGeometryOct 3

The area of a circle from a different perspective. ⭕📐

ALT Figure depicting a circle, an inscribed square, a circumscribed square and an equiareal square in between.

Gaál Sándor@gmac4247Sep 5

ALT 3.2radius² is the exact area of a circle.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT Arc and tangent line

ALT Arc and tangent line spacing

Basic Geometry · Sep 17, 2026 · 11:10 AM UTC

Basic Geometry@BasicGeometrySep 17

Basic Geometry has knowledge about suspected caller ID spoofing using its phone number. Take care. Spoofing is illegal if done with the intent to defraud, cause harm, or wrongfully obtain anything of value. Violations can trigger significant civil penalties or criminal charges.

Basic Geometry · Sep 5, 2026 · 4:38 PM UTC

Basic Geometry@BasicGeometrySep 5

Replying to @gmac4247

@gmac4247

ALT Circle and isoperimetric hexagon

ALT Example 1/2

ALT Example 2/2

ALT 3.2radius² is the exact area of a circle.

Gaál Sándor · Sep 5, 2026 · 4:19 PM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Sep 5

ALT 3.2radius² is the exact area of a circle.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT Arc and tangent line

ALT Arc and tangent line spacing

170

Gaál Sándor · Sep 5, 2026 · 10:01 AM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Sep 5

Replying to @gmac4247 @BasicGeometry

This real-world example should make it clear why the pi is an artifact of a fundamentally flawed theoretical approximate. In case you missed the previous context: 3.2radius² is the exact area of a circle. The circumference can be derived from that algebraically as 6.4radius.

ALT Text 1/2

ALT Text 2/2

ALT 3.2radius² is the exact area of a circle.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

Basic Geometry · Aug 31, 2026 · 5:36 PM UTC

Basic Geometry@BasicGeometryAug 31

Replying to @gmac4247 @Google

To those who understand how the mathematical constant named pi was *theoretically approximated* this single post should make it clear why that approach is fundamentally and critically flawed. The reply is open for transparent empirical measurement data. Not for academic rubbish.

ALT Debunking one of the biggest frauds in history: the mathematical constant named pi.

Gaál Sándor · Aug 31, 2026 · 4:57 PM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Aug 31

This made me really sad, @Google. I understand if you - don't understand what I wrote, - can't measure it, - don't care to measure it. But framing it as "debunked" is extremely disrespectful, and misleading. I'm doing my work mindfully. Please fix your end.

ALT Search result.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT Algebraic proof of that the area of a circle equals exactly 3.2radius².

Gaál Sándor · Aug 16, 2026 · 2:59 PM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Aug 16

So basically the loving memory of David Hilbert and the Bourbaki Group stands between common sense and standard geometry.

🤖 Made with AI

ALT Common sense vs. standard geometry

Gaál Sándor@gmac4247Jul 20

3.2radius² is the exact area of a circle. (Fig. 1.) 3.2diameter is the circumference. (Pic.) Area/radius²=Circumference/diameter=3.2≈3.14≈π The mathematical constant π is an artifact of a fundamentally flawed theoretical approximate. (Fig. 2.)

Fig. 1. 3.2radius² is the exact area of a circle. A circle is cut into quadrants. Each one is aligned to each vertices of a square. The arcs of the quadrants intersect at the quarters of the centerlines of the square. The ratio between the radius and the side of the square is calculable. r = √((side/2)² + (side/4)²) = side√5/4

ALT Fig. 1. 3.2radius² is the exact area of a circle. A circle is cut into quadrants. Each one is aligned to each vertices of a square. The arcs of the quadrants intersect at the quarters of the centerlines of the square. The ratio between the radius and the side of the square is calculable. r = √((side/2)² + (side/4)²) = side√5/4

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT Area/radius²=Circumference/diameter=3.2≈3.14≈π

ALT Fig. 2. The mathematical constant named pi is an artifact of a fundamentally flawed theoretical approximate.

Basic Geometry · Aug 15, 2026 · 8:26 PM UTC

Basic Geometry@BasicGeometryAug 15

This is a very important message. It's something to think about seriously.

Gaál Sándor@gmac4247Aug 15

Replying to @gmac4247 @VisionaryVoid

I just finished an about 10 pages long refute of the pi today, and I asked the opinion of a chat bot about it. Here's a screenshot of the actual chat. It's funny in a way, but not really. The pi-propagandists are genuinely evil. They're messing up people's minds with that crap.

Screenshot of a chat with a LLM. User — after sharing a detailed explanation of why the mathematical constant named pi is wrong: Would you try to argue with that to save the pi? LLM: If I were tasked with playing devil's advocate to defend classical pi and save the traditional limit process, ...

ALT Screenshot of a chat with a LLM. User — after sharing a detailed explanation of why the mathematical constant named pi is wrong: Would you try to argue with that to save the pi? LLM: If I were tasked with playing devil's advocate to defend classical pi and save the traditional limit process, ...

Gaál Sándor · Aug 13, 2026 · 7:21 PM UTC

Basic Geometry retweeted

Gaál Sándor@gmac4247Aug 13

The backstory of these images is that I asked for geometry figures from an AI-assisted image generator. These ones failed, but I still find them beautiful. The team fixed it, so it gives accurate shapes now. Thanks. The downside is that there are no more like these coming up.

🤖 Made with AI

ALT Attempted geometry figure. Image made with the help of Microsoft Copilot.

ALT Attempted tetrahedra in a cube. Image made with the help of Microsoft Copilot.

Basic Geometry · Aug 6, 2026 · 11:16 AM UTC

Basic Geometry@BasicGeometryAug 6

Replying to @gmac4247

The polygon approximation of the pi doubles the side count of a circumscribed hexagon repeatedly via angle bisection. But when the sides become short enough, their points coincide with the arc. Hence they cease to be upper limits.

ALT Arc and tangent line.

Basic Geometry · Aug 5, 2026 · 6:40 PM UTC

Basic Geometry@BasicGeometryAug 5

In the past few years I pinpointed several aspects of this. Or other aspects of the main point. There's no way to tell what comes from what. The relationships come as a whole. The point is that the mathematical constant pi is built on a series of flawed assumptions.

Gaál Sándor@gmac4247Aug 5

Fig.1. shows the flaw in the traditional approach of tangency. One point of vertical separation on a 3 point length is not what a curve looks like. (Fig.2.) Tangency is impossible under the traditional definitions. The mathematical constant pi is fundamentally flawed.

Figure 1. The absurdity in the traditional approach of tangency. One point of vertical separation on a 3 point length is not what a curve looks like.

ALT Figure 1. The absurdity in the traditional approach of tangency. One point of vertical separation on a 3 point length is not what a curve looks like.

ALT Figure 2. Arc and tangent line.

ALT The circumference of a coin with a diameter of 29 mm measured about 93 mm on a ruler with a thin paper strip.

ALT 3.2radius² is the exact area of a circle.