Matthew Arcus
@matthewarcus.bsky.social
2026 = 45²+1 which is exactly the number of coloured boxes in this image - and there are exactly 45 of each type of box, except the empty red box on the top left,which is unique. See oeis.org/A002522 for more details.
January 1, 2026 at 9:15 PM
2026 = 45²+1 which is exactly the number of coloured boxes in this image - and there are exactly 45 of each type of box, except the empty red box on the top left,which is unique. See oeis.org/A002522 for more details.
A nice variation on the traditional proof of Heron's formula. Given triangle ABC with incentre I, construct IG perpendicular to BI & complete the diagram as shown. Similar triangles show that LG = βγ/r and Euclid I.43 does the rest:
January 6, 2025 at 8:33 AM
A nice variation on the traditional proof of Heron's formula. Given triangle ABC with incentre I, construct IG perpendicular to BI & complete the diagram as shown. Similar triangles show that LG = βγ/r and Euclid I.43 does the rest:
A nice visual demonstration that 2025 = 45² = (1+2+3+4+5+6+7+8+9)² = 1³+2³+3³+4³+5³+6³+7³+8³+9³:
December 28, 2024 at 7:52 PM
A nice visual demonstration that 2025 = 45² = (1+2+3+4+5+6+7+8+9)² = 1³+2³+3³+4³+5³+6³+7³+8³+9³: