{"id":165776,"date":"2023-06-14T19:24:27","date_gmt":"2023-06-15T00:24:27","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2023\/06\/math-you-can-wear-fibonacci-spiral-led-badge"},"modified":"2023-06-14T19:24:27","modified_gmt":"2023-06-15T00:24:27","slug":"math-you-can-wear-fibonacci-spiral-led-badge","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2023\/06\/math-you-can-wear-fibonacci-spiral-led-badge","title":{"rendered":"Math You Can Wear: Fibonacci Spiral LED Badge"},"content":{"rendered":"<p><\/p>\n<p><iframe style=\"display: block; margin: 0 auto; width: 100%; aspect-ratio: 4\/3; object-fit: contain;\" src=\"https:\/\/www.youtube.com\/embed\/2Py-FlRIieQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope;\n   picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>Fibonacci numbers are seen in the natural structures of various plants, such as the florets in sunflower heads, areoles on cacti stems, and scales in pine cones. [HackerBox] has developed a <a href=\"https:\/\/www.instructables.com\/HackerBox-0091-Fibonacci\/\" target=\"_blank\">Fibonacci Spiral LED Badge<\/a> to bring this natural phenomenon to your electronics.<\/p>\n<p>To position each of the 64 addressable LEDs within the PCB layout, [HackerBox] computed the polar (r,\u03b8) coordinates in a spreadsheet according to the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Fermat%27s_spiral\" target=\"_blank\">Vogel model<\/a> and then converted them to rectangular (x, y) coordinates. A little more math translates the points \u201coff origin\u201d into the center of the PCB space and scale them out to keep the first two 5 mm LEDs from overlapping. Finally, the LED coordinates were pasted into the KiCad PCB design file.<\/p>\n<p>An RP2040 microcontroller controls the show, and a switch on the badge selects power between USB and three AA batteries and a DC\/DC boost converter. The PCB also features two capacitive touch pads. [HackerBox] has published the KiCad files <a href=\"https:\/\/github.com\/h4ck3rb0x\/HackerBox0091\" target=\"_blank\">for the badge<\/a>, and the CircuitPython firmware is <a href=\"https:\/\/www.instructables.com\/HackerBox-0091-Fibonacci\/\" target=\"_blank\">shared with the project<\/a>. If C\/C++ is more your preference, the RP2040 MCU can also be programmed using the Arduino IDE.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fibonacci numbers are seen in the natural structures of various plants, such as the florets in sunflower heads, areoles on cacti stems, and scales in pine cones. [HackerBox] has developed a Fibonacci Spiral LED Badge to bring this natural phenomenon to your electronics. To position each of the 64 addressable LEDs within the PCB layout, [\u2026]<\/p>\n","protected":false},"author":662,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1497,2229,8],"tags":[],"class_list":["post-165776","post","type-post","status-publish","format-standard","hentry","category-energy","category-mathematics","category-space"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/165776","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=165776"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/165776\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=165776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=165776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=165776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}