{"type":"rich","version":"1.0","provider_name":"Transistor","provider_url":"https://transistor.fm","author_name":"Science Tech Brief By HackerNoon","title":"Exploring Hockey Stick Theorems: Proof of Results and References","html":"<iframe width=\"100%\" height=\"180\" frameborder=\"no\" scrolling=\"no\" seamless src=\"https://share.transistor.fm/e/6818ce43\"></iframe>","width":"100%","height":180,"duration":127,"description":"\n        This story was originally published on HackerNoon at: https://hackernoon.com/exploring-hockey-stick-theorems-proof-of-results-and-references.\n             Investigating hockey stick theorems in Pascal's and trinomial triangles, revealing patterns akin to ball trajectories in combinatorial mathematics. \n            Check more stories related to science at: https://hackernoon.com/c/science.\n            You can also check exclusive content about #math, #pascal's-triangle, #trinomial-triangle, #hockey-stick-theorem, #combinatorial-mathematics, #mathematical-theorems, #pascal's-identity, #mathematical-patterns,  and more.\n            \n            \n            This story was written by: @hockeystick. Learn more about this writer by checking @hockeystick's about page,\n            and for more stories, please visit hackernoon.com.\n            \n                \n                \n                In the proof of both theorems, we use induction. This paper is available on arxiv(https://arxiv.org/abs/1404.5106) under CC BY 4.0 DEED license. The hockey stick theorem in the trinomial triangles has been proved. It can be translated in Pascal pyramid as follows.\n        \n        ","thumbnail_url":"https://img.transistorcdn.com/S66fL9skYMhlajDauLWqBH_bXds_u8JsPbvAZlh45OA/rs:fill:0:0:1/w:400/h:400/q:60/mb:500000/aHR0cHM6Ly9pbWct/dXBsb2FkLXByb2R1/Y3Rpb24udHJhbnNp/c3Rvci5mbS9zaG93/LzQxMjczLzE2ODM1/ODI0MjQtYXJ0d29y/ay5qcGc.webp","thumbnail_width":300,"thumbnail_height":300}