Basic Geometry (@BasicGeometry) header
Basic Geometry (@BasicGeometry) profile picture

Basic Geometry

@BasicGeometry

Providing the Core Geometric System ™, the essential framework for geometric understanding.

 Szentendre
basic-geometry.pages.dev
Joined April 2023
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  • Following8
  • Followers18
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.
3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle.

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

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

Circle and square area comparison.

ALT Circle and square area comparison.

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

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

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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.
3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle.

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

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

Circle and square area comparison.

ALT Circle and square area comparison.

Circle and square area comparison.

ALT Circle and square area comparison.

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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.
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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.
Circle and square area comparison

ALT Circle and square area comparison

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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.
Circle area diagram

ALT Circle area diagram

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 1/3

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 2/3

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

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

Gaál Sándor (@gmac4247) profile pictureGaál 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.
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The area of a circle from a different perspective. ⭕📐
Figure depicting a circle, an inscribed square, a circumscribed square and an equiareal square in between.

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

Gaál Sándor (@gmac4247) profile pictureGaál 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.
3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle.

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

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

Arc and tangent line

ALT Arc and tangent line

Arc and tangent line spacing

ALT Arc and tangent line spacing

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Replying to @gmac4247
@gmac4247
Circle and isoperimetric hexagon

ALT Circle and isoperimetric hexagon

Example 1/2

ALT Example 1/2

Example 2/2

ALT Example 2/2

3.2radius² is the exact area of a circle.

ALT 3.2radius² is the exact area of a circle.

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

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

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

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

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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.
Arc and tangent line.

ALT Arc and tangent line.

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Replying to @gmac4247
Mainstream geometry insists that a tangent line can always be drawn. A tangent line coincides with a circle only at a single point. Yet, when attempting to circumscribe a 24-sided polygon about a circle, each side coincides with the arc along a significant section.
Attempting to circumscribe a 24-sided polygon about a circle.

ALT Attempting to circumscribe a 24-sided polygon about a circle.

Zooming in on one side of an attempted 24-sided circumscribed polygon about a circle.

ALT Zooming in on one side of an attempted 24-sided circumscribed polygon about a circle.

When attempting to circumscribe a 24-sided polygon about a circle, each side coincides with the arc along a significant section

ALT When attempting to circumscribe a 24-sided polygon about a circle, each side coincides with the arc along a significant section

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