Hypercomplex numbers | Math History | NJ Wildberger

In the 19th century, the geometrical aspect of the complex numbers became generally appreciated, and mathematicians started to look for higher dimensional examples of how arithmetic interacts with geometry. A particularly interesting development is the discovery of quaternions by W. R. Hamilton, and the subsequent discovery of octonians by his friend Graves and later by A. Cayley. Surprisingly perhaps the arithmetic of these 4 and 8 dimensional extensions of complex numbers are intimately connected with number theoretical formulas going back to Diophantus, Fibonacci and Euler. ************ Research Gate page: https://www.researchgate.net/profile/Norman_Wildberger Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon: https://www.patreon.com/njwildberger Your support would be much appreciated. Wild Egg Maths YT channel: https://www.youtube.com/channel/UCriFv3G22iOUidUhkIGXuh Insights into Mathematics Playlists: https://www.youtube.com/playlist?list=PLIljB45xT85CL0-5wO4P-OwuH7SzBUyC0 (31 videos) https://www.youtube.com/playlist?list=PLIljB45xT85B0aMG-G9oqj-NPIuBMnq8z (18 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DHcleY93bd2WlywQYxHv7H (6 videos) https://www.youtube.com/playlist?list=PLIljB45xT85AZjh2GUdwsMuAWTEHXCLb- (4 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DeX148Q2T2elycnIYHTxdP (44 videos) https://www.youtube.com/playlist?list=PLIljB45xT85A6D0eylgAM4Xc1b_dDTgHW (8 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DGxj1x_dyaSggbauAgrB6R (226 videos) https://www.youtube.com/playlist?list=PLIljB45xT85A_VZD126sND3XECDSI-qGs (26 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DfokRNdx5eQ_qA43BwyM-_ (45 videos) https://www.youtube.com/playlist?list=PLIljB45xT85CvrEUnhS4dkTm9Lci5JTYS (43 videos) https://www.youtube.com/playlist?list=PLIljB45xT85D7wczwyUQdwDe2duZ7wPTf (40 videos) https://www.youtube.com/playlist?list=PLIljB45xT85Ar_tuHmRDI2Xr5tWOTI1oW (55 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DPSrQpExd2L870ggxd2KEB (34 videos) https://www.youtube.com/playlist?list=PLIljB45xT85C3-5f6-qQS3YhgygZgnGYs (8 videos) https://www.youtube.com/playlist?list=PLIljB45xT85D7hfVLKyEJbQxOJ4yYm1-9 (9 videos) https://www.youtube.com/playlist?list=PLIljB45xT85BtiJIcDF2uuFc7_ndd1UL6 ( 46 videos) https://www.youtube.com/playlist?list=PLIljB45xT85B6MYBrWldlJ3w-Q1LaEdoy (40 videos) https://www.youtube.com/playlist?list=PLIljB45xT85DIpzaWggqJDIK8m2u09dQL (7 videos) https://www.youtube.com/playlist?list=PLIljB45xT85Ag6ragdmHaxUOKcQsIsrXZ (7 videos) https://www.youtube.com/playlist?list=PLIljB45xT85A5w_vZ5BB1IQAxAMhz5o5S (19 videos) https://www.youtube.com/playlist?list=PLIljB45xT85BjhYV7QswANMF3gKPx9BqT (21 videos) https://www.youtube.com/playlist?list=PLIljB45xT85Bi7PvrTkAaAswTwsfsR5HV (10 videos) https://www.youtube.com/playlist?list=PLIljB45xT85CyF_7bKd6y36VArOy3p2oh (94 videos) Wild Egg Maths Playlists: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5m3XKK0OPc31l-GTqDiAjs (4 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz4CVqTYS1fwInPOZxBxDaQf (64 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz7PpsRFHuGb3EhwZtEOdRjV (45 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz6HqaFPB4HTZOQ8jgDAVnuz (20 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz71VHhAIUN-7Y6-JVcwF-xA (8 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz75-t4UaYvHwPe5AHGA_EWe (9 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz5W25vaXSreTMTwpPhWs1w2 (52 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz4DCenuIAr9R2kXLq4ywRAm (9 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz7OynfQubQrYkxYurauO-HD (14 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz7cyg5JdKBpzB4fTQT7f-Xl (8 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz5Bcq1VN_R7zYDZH3u49FH8 (25 videos) https://www.youtube.com/playlist?list=PLzdiPTrEWyz5flY1TFd7cekRMZRvPGkzM (30 videos)