{"title":"Beyond the Quadratic:","authors":"","doi":"10.2307/j.ctvc774cp.22","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.22","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127320473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Combinatorial Problem with Physics Implications:","authors":"","doi":"10.2307/j.ctvc774cp.14","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.14","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125289097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
1 The greatest common divisor Consider two positive integers a0 > a1. The greatest common divisor of a0 and a1, denoted gcd(a0, a1) is the largest positive integer g such that g|a0 and g|a1, i.e. g divides both a0 and a1. Observation 1: The gcd(a0, a1) always exists. Observation 2 (Euclid): Let a0 = q1a1 + r where 0 ≤ r < a1 (note that this representation is always possible and unique), then gcd(a0, a1) = gcd(a1, r). The proof of this fact consists of showing that d|a0 and d|a1 ⇔ d|a1 and d|r.
{"title":"The Euclidean Algorithm:","authors":"S. Mneimneh","doi":"10.2307/j.ctvc774cp.28","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.28","url":null,"abstract":"1 The greatest common divisor Consider two positive integers a0 > a1. The greatest common divisor of a0 and a1, denoted gcd(a0, a1) is the largest positive integer g such that g|a0 and g|a1, i.e. g divides both a0 and a1. Observation 1: The gcd(a0, a1) always exists. Observation 2 (Euclid): Let a0 = q1a1 + r where 0 ≤ r < a1 (note that this representation is always possible and unique), then gcd(a0, a1) = gcd(a1, r). The proof of this fact consists of showing that d|a0 and d|a1 ⇔ d|a1 and d|r.","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126961933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Falling Raindrop, Variable-Mass Problem:","authors":"","doi":"10.2307/j.ctvc774cp.21","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.21","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128225126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Acknowledgments","authors":"","doi":"10.2307/j.ctvc774cp.35","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.35","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116147525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Another Cubic Equation:","authors":"","doi":"10.2307/j.ctvc774cp.23","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.23","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121623564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"When the Computer Fails:","authors":"","doi":"10.2307/j.ctvc774cp.18","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.18","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126508404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Wizard Math:","authors":"","doi":"10.2307/j.ctvc774cp.27","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.27","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128193745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Beyond the Cubic:","authors":"","doi":"10.2307/j.ctvc774cp.24","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.24","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132099057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Escaping an Atomic Explosion:","authors":"","doi":"10.2307/j.ctvc774cp.25","DOIUrl":"https://doi.org/10.2307/j.ctvc774cp.25","url":null,"abstract":"","PeriodicalId":365299,"journal":{"name":"How to Fall Slower Than Gravity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124330823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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