Uploaded May 2025 | Updated September 2026, 2 weeks ago
This video is a compilation of eight animations 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: buymeacoffee.com/VisualProofs. Thanks!
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).
Infinite sum of powers of 1/2 (0.111... = 1 in base 2): youtube.com/shorts/iVLE8gEJfPA
This animation is based on a visual proof by Warren Page from the September 1981 issue of Mathematics Magazine, (page 201 - jstor.org/stable/2689632 ).
Infinite sum of powers of 1/3 (0.222... = 1 in base 3):
youtube.com/shorts/GwIVlNRV-M0
This animation is based on a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (doi.org/10.2307/2690738).
Infinite sum of powers of 1/4 (0.333... = 1 in base 4):
youtube.com/shorts/qk1IPvvWfr0
This animation is based on a proof by Sunday A. Ajose from the June 1994 issue of Mathematics Magazine (jstor.org/stable/2690616 page 230).
Infinite sum of powers of 1/5 (0.444... = 1 in base 5):
youtube.com/shorts/PAJMMS-J2SY
This animation is based on a proof by Rick Mabry from his website lsusmath.rickmabry.org/rmabry/fivesquares/fsq2.gif and featured in Roger B. Nelsen's third Proofs Without Words compendium (bookstore.ams.org/clrm-52/).
Infinite sum of powers of 1/6 (0.555... = 1 in base 6):
youtube.com/shorts/T2Mi0AUIKJY
This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (jstor.org/stable/27646594).
Infinite sum of powers of 1/7 (0.666... = 1 in base 7):
youtube.com/shorts/4ri5pCirFsQ
This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (doi.org/10.1080/07468342.2020.1830649 p. 385)
Infinite sum of powers of 1/8 (0.777... = 1 in base 8):
youtube.com/shorts/8TDSID0BhwI
This animation is based on a visual proof from Roger B. Nelsen in the February 2006 issue of Mathematics Magazine (doi.org/10.2307/27642904 or jstor.org/stable/27642904), page 60.
Infinite sum of powers of 1/9 (0.888... = 1 in base 9):
youtu.be/nQb11RIEXkI
To learn more about animating with manim, check out:
https://manim.community
This video is a compilation of eight animations 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: buymeacoffee.com/VisualProofs. Thanks!
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).
Infinite sum of powers of 1/2 (0.111... = 1 in base 2): youtube.com/shorts/iVLE8gEJfPA
This animation is based on a visual proof by Warren Page from the September 1981 issue of Mathematics Magazine, (page 201 - jstor.org/stable/2689632 ).
Infinite sum of powers of 1/3 (0.222... = 1 in base 3):
youtube.com/shorts/GwIVlNRV-M0
This animation is based on a proof by Elizabeth M. Markham from the October 1993 issue of Mathematics Magazine page 242 (doi.org/10.2307/2690738).
Infinite sum of powers of 1/4 (0.333... = 1 in base 4):
youtube.com/shorts/qk1IPvvWfr0
This animation is based on a proof by Sunday A. Ajose from the June 1994 issue of Mathematics Magazine (jstor.org/stable/2690616 page 230).
Infinite sum of powers of 1/5 (0.444... = 1 in base 5):
youtube.com/shorts/PAJMMS-J2SY
This animation is based on a proof by Rick Mabry from his website lsusmath.rickmabry.org/rmabry/fivesquares/fsq2.gif and featured in Roger B. Nelsen's third Proofs Without Words compendium (bookstore.ams.org/clrm-52/).
Infinite sum of powers of 1/6 (0.555... = 1 in base 6):
youtube.com/shorts/T2Mi0AUIKJY
This animation is based on a proof by James Tanton from the March 2008 issue of The College Mathematics Journal page 106. (jstor.org/stable/27646594).
Infinite sum of powers of 1/7 (0.666... = 1 in base 7):
youtube.com/shorts/4ri5pCirFsQ
This animation is based on a proof by Stephan Berendonk (2020) from the November 2020 issue of The College Mathematics Journal, (doi.org/10.1080/07468342.2020.1830649 p. 385)
Infinite sum of powers of 1/8 (0.777... = 1 in base 8):
youtube.com/shorts/8TDSID0BhwI
This animation is based on a visual proof from Roger B. Nelsen in the February 2006 issue of Mathematics Magazine (doi.org/10.2307/27642904 or jstor.org/stable/27642904), page 60.
Infinite sum of powers of 1/9 (0.888... = 1 in base 9):
youtu.be/nQb11RIEXkI
To learn more about animating with manim, check out:
https://manim.community
