0.bbbb... = 1 (in base b+1) | 9 geometric series dissection proofs without words скачать в хорошем качестве

0.bbbb... = 1 (in base b+1) | 9 geometric series dissection proofs without words

This video is a compilation of nine shorter videos I have created showing dissection proofs for infinite geometric series with ratio of the form 1/n and first term 1/n. One interpretation of these series is that 0.bbbb... = 1 in base b+1 . If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks! For another compilation of geometric series dissections (with minimal overlaps), check out this video:    • Beautiful Geometry behind Geometric S...   This is a compilation of nine shorts (most with words). If you want to see those, the links are below (along with attribution to the original ``proof without words" author). 00:06 Infinite sum of powers of 1/2 (0.111... = 1 in base 2):    • 0.1111… = 1 (in base 2)   This animation is based on a visual proof by Warren Page from the September 1981 issue of Mathematics Magazine, (page 201 - https://www.jstor.org/stable/2689632 ). 00:38 Infinite sum of powers of 1/3 (0.222... = 1 in base 3):    • 0.2222…= 1 (in base 3)   This animation is based on a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (https://doi.org/10.2307/2690738). 01:20 Infinite sum of powers of 1/4 (0.333... = 1 in base 4):    • 0.3333… = 1 (in base 4)   This animation is based on a proof by Sunday A. Ajose from the June 1994 issue of Mathematics Magazine (https://www.jstor.org/stable/2690616 page 230). 01:55 Infinite sum of powers of 1/5 (0.444... = 1 in base 5):    • 0.4444... = 1 (in base 5)   This animation is based on a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (https://doi.org/10.2307/2690738). 02:40 Infinite sum of powers of 1/6 (0.555... = 1 in base 6):    • 0.5555… = 1 (in base 6)   This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594). 03:20 Infinite sum of powers of 1/7 (0.666... = 1 in base 7):    • 0.66666… = 1 (in base 7)   This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (https://doi.org/10.1080/07468342.2020... p. 385) 04:15 Infinite sum of powers of 1/8 (0.777... = 1 in base 8):    • 0.7777… = 1 (in base 8)   This animation is based on a visual proof from Roger B. Nelsen in the February 2006 issue of Mathematics Magazine (https://doi.org/10.2307/27642904 or https://www.jstor.org/stable/27642904), page 60. 05:00 Infinite sum of powers of 1/9 (0.888... = 1 in base 9):    • 0.8888… = 1 (in base 9)   This animation is inspired by the a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (https://doi.org/10.2307/2690738). 05:50 Infinite sum of powers of 1/10 (0.999... = 1 in base 10):    • 0.999999… = 1   This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (https://www.jstor.org/stable/27646594). To learn more about animating with manim, check out: https://manim.community ___________________________________ Music: Wanderer by Alexander Nakarada (CreatorChords) | https://creatorchords.com Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/...