[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"branding":3,"analytics":7,"article-new-formulas-push-pi-calculation-efficiency-to-record-lows":10,"sections":35},{"siteName":4,"siteTagline":5,"publisherName":4,"contactEmail":6},"The Revision","Tech news, decoded.","editor@therevision.news",{"gaMeasurementId":8,"adsenseClientId":9},"G-ZW2MV82GYR","ca-pub-8533917693782264",{"article":11},{"id":12,"slug":13,"title":14,"dek":15,"body_md":16,"tags_json":17,"published_at":18,"created_at":19,"updated_at":20,"status":21,"review_note":22,"review_notes":23,"image_url":22,"persona_id":22,"persona_name":22,"section":24,"tags":25,"sources":30,"feedback":34,"feedback_at":22,"cost_usd":34,"total_tokens":34},6688,"new-formulas-push-pi-calculation-efficiency-to-record-lows","New Formulas Push Pi Calculation Efficiency to Record Lows","A new search algorithm found pi formulas more efficient than any known before, though the real-world payoff is mostly bragging rights.","Mathematicians just found more efficient ways to calculate pi - the old-fashioned way.\n\nMachin-like formulas are equations that add up simple arctangent functions to compute pi, a technique dating back to the 1700s. Researchers built a search tool that combines the PSLQ algorithm, which hunts for hidden mathematical relationships between numbers, with filters based on Gaussian integers (complex numbers with whole-number parts) to narrow the search space. That let them scan far more candidate formulas than earlier searches could handle. The result: a five-term formula with a Lehmer measure of 1.4572 and a six-term formula at 1.3291, both the lowest ever recorded for their length, where a lower measure means less arithmetic work per digit of pi produced.\n\nThis isn't about breaking pi digit-count records - Chudnovsky-style algorithms already do that faster. What matters here is the search method: constrained PSLQ turns an old, mostly hand-tuned corner of math into something a computer can systematically improve, and the same approach can be extended to hunt for even longer, more efficient formulas.\n\nIt's a reminder that centuries-old math problems still have unclaimed territory, if you're willing to throw enough compute at Gaussian integers.","[\"pi\",\"mathematics\",\"number-theory\",\"algorithms\"]","2026-09-17T04:00:00.000Z","2026-09-18T06:10:03.003Z","2026-09-18T06:10:14.914Z","published",null,[],"science",[26,27,28,29],"pi","mathematics","number-theory","algorithms",[31],{"name":32,"url":33},"arXiv cs.AI","https:\u002F\u002Farxiv.org\u002Fabs\u002F2508.08307",0,{"sections":36},[37,42,46,51,56,60,63,68,73,77,82,87,92,97],{"name":38,"slug":39,"count":40,"latest_published_at":41},"AI","ai",3852,"2026-09-17T08:27:09.000Z",{"name":43,"slug":44,"count":45,"latest_published_at":18},"Security","security",648,{"name":47,"slug":48,"count":49,"latest_published_at":50},"Policy","policy",338,"2026-09-11T04:00:00.000Z",{"name":52,"slug":53,"count":54,"latest_published_at":55},"Deals","deals",179,"2026-06-29T20:02:07.000Z",{"name":57,"slug":58,"count":59,"latest_published_at":18},"Hardware","hardware",154,{"name":61,"slug":24,"count":62,"latest_published_at":18},"Science",114,{"name":64,"slug":65,"count":66,"latest_published_at":67},"Consumer Tech","consumer-tech",99,"2026-09-09T17:27:33.000Z",{"name":69,"slug":70,"count":71,"latest_published_at":72},"Software","software",75,"2026-09-10T20:41:21.000Z",{"name":74,"slug":75,"count":76,"latest_published_at":18},"Dev Tools","dev-tools",73,{"name":78,"slug":79,"count":80,"latest_published_at":81},"Startups","startups",55,"2026-09-09T23:14:29.000Z",{"name":83,"slug":84,"count":85,"latest_published_at":86},"Gaming","gaming",43,"2026-09-10T12:18:06.000Z",{"name":88,"slug":89,"count":90,"latest_published_at":91},"General","general",41,"2026-09-08T01:57:23.000Z",{"name":93,"slug":94,"count":95,"latest_published_at":96},"Reviews","reviews",20,"2026-06-24T12:00:01.000Z",{"name":98,"slug":99,"count":100,"latest_published_at":101},"How-To","how-to",6,"2026-06-16T09:00:00.000Z"]