Geometry Insights
@geometryupdates
Revealing the Architecture of Mathematics 64 Premium GCSE & A-Level Articles and Counting By failing to prepare, you are preparing to fail. — Benjamin Franklin
Two chords cross inside a circle, splitting into four segments. Surprisingly, the lengths obey a strict balance: one product equals the other. I rebuild the chord theorem from first principles, showing how angle symmetry forces the identity. geometryinsights.wordpress.com/2025/12/22/int…
One vector 𝐀 defines a whole stack of planes perpendicular to it. The scalar λ just picks the sheet. Starting from (𝐏 − λ𝐀) ⟂ 𝐀, the dot product collapses it to 𝐀·𝐏 = λ∥𝐀∥². geometryinsights.wordpress.com/2025/12/21/the…
The î–ĵ–k̂ cross-product “rules” aren’t six things to memorise. They encode orientation in ℝ³. Pick î→ĵ→k̂ as positive: follow the cycle ⇒ +, reverse ⇒ −, same ⇒ 0. One structure generates the whole table. geometryinsights.wordpress.com/2025/12/21/the…
The Möbius strip constructed using Desmos 3D. en.wikipedia.org/wiki/M%C3%B6bi… #trigonometry #parametricsurfaces #vectors #Desmos3D
Geometry: How to Prove The Chord Theorem, ab=cd, Full Explanation #circletheorem #visualmath youtu.be/vl7CsHENTc8?si…
youtube.com
YouTube
Geometry: How to Prove The Chord Theorem, ab=cd, Full Explanation...
Build a torus in ℝ³ from first principles: take a circle in the (r,z) plane and rotate it around the z-axis. v moves around the circle, u performs the rotation. Key constraint: r ≥ 0 (it becomes the x,y radius). geometryinsights.wordpress.com/2025/12/13/how…
Torus in ℝ³, generated by two circles (one sets the ring, one sets r and z). Clean parametric build: ((a + d cos v) cos u, (a + d cos v) sin u, b + d sin v), with 0 ≤ u,v ≤ 2π and a ≥ d. instagram.com/p/DSPdDQXjHxt/
You can also access another 80+ articles plus resources on Geometric Bites (free): geometricbites.blogspot.com/p/all-articles… This is just the start.
The 60th article was dropped today. Everything is derived, there are no assumptions. All the theories stack up, forming the foundations of more advanced theories. It's all being built from the bottom up. It's not about chucking numbers into formulas, it's about understanding.
Completing the Square from the Square (x+y)² “Completing the square” is really just area bookkeeping inside a square of side x+y. One clean cut explains the identity and shows why the quadratic trick works. geometryinsights.wordpress.com/2025/12/12/com…
The Turning Point of a Quadratic Curve If you complete the square for y = ax² + bx + c (a ≠ 0), you can locate the turning point quickly without calculus: (−b/(2a), c − b²/(4a)) geometryinsights.wordpress.com/2025/12/12/the…
Geometry Insights bridges the gap between A-Level, Further Pure and University Mathematics. If you're doing your A-Levels and you're looking for more rigorous and detailed explanations, this is the project to be part of. #scaffolding
More free resources for students: A-Level Real Intervals Read here: geometricbites.blogspot.com/p/a-level-real… There will be more free content provided, and for premium instructions and explanations, visit: @geometryupdates .
New article: Reconstructing a Quadratic Sequence from Its First Three Terms (11 Dec 2025). From f(n)=an²+bn+c with a≠0, you can recover a,b,c using just f(1),f(2),f(3). geometryinsights.wordpress.com/2025/12/11/rec…
Functions are more than bare formulas like y = x² + 1. “The Six Essential Pieces of a Function” uses a cone’s volume and a simple quadratic to show how formula, signature, notation, domain, codomain, and rule all fit together. Link: geometryinsights.wordpress.com/2025/12/10/the…
Rows vs columns: two directions, one grid. If you’ve ever been unsure which is which (or what an “array” really is), this article walks through it with tiny examples and memory tricks. Full explanation: geometryinsights.wordpress.com/2025/12/10/row…
New article: “Shadows on the Axes: Coordinate Projections in ℝ²”. Every point (a, b) in the plane casts two shadows on the axes. We unpack the projection maps π_x and π_y, from basic coordinates to vectors, matrices, and graphs. 🔗 geometryinsights.wordpress.com/2025/12/09/sha…
Distance is orientation-free. Switching A and B flips the vector but not its length: ||A−B|| = ||B−A|| in ℝ³ and beyond. Read more: Why ∥A − B∥ = ∥B − A|| in ℝ³ (and Beyond) geometryinsights.wordpress.com/2025/12/09/why…
Two non-zero vectors from the origin in ℝ² define a rigid triangle and a unique interior angle. Starting from that triangle and the law of cosines, we recover the dot-product angle formula and turn it into a single Desmos definition. geometryinsights.wordpress.com/2025/12/08/the…
United States เทรนด์
- 1. FINALLY DID IT 761 B posts
- 2. The PENGU 242 B posts
- 3. The Jupiter 191 B posts
- 4. Thor 36,4 B posts
- 5. The BONK 105 B posts
- 6. #LingOrmHNYatICONSIAM 854 B posts
- 7. Brees 1.335 posts
- 8. Kuechly N/A
- 9. Witten N/A
- 10. Good Tuesday 36,9 B posts
- 11. Fred Taylor N/A
- 12. Vinatieri N/A
- 13. Chip Kelly 1.179 posts
- 14. #tuesdayvibe 2.299 posts
- 15. Frank Gore N/A
- 16. Fitzgerald 2.228 posts
- 17. Pro Football Hall of Fame 1.887 posts
- 18. Chao Phraya 10,8 B posts
- 19. The 4D 28,5 B posts
- 20. Willie Anderson N/A
Something went wrong.
Something went wrong.