30:[] 2e:{"title":"Fibonacci","cells":[{"id":0,"value":"md`# Fibonacci`","pinned":false,"hidden":false,"mode":"ojs"},{"id":142,"value":"intro = html`\n

\nIn the Fibonacci numbers sequence every number after the first two is the sum of the two preceding numbers:\n

\n0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 80, 144, ...\n

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":200,"value":"formula = md`${tex`F_{n} = F_{n-1} + F_{n-2}`}\n\nwith seed values:\n\n${tex`F_0 = 0, F_1 = 1`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":144,"value":"wiki = md`You can read more about Fibonacci numbers here:\n\nhttps://en.wikipedia.org/wiki/Fibonacci_number`","pinned":false,"hidden":false,"mode":"ojs"},{"id":147,"value":"html`

Generate Fiboncacci Numbers

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"viewof iterations = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":28,"value":"function fibs(count) {\n let f = [0, 1];\n for (let i=2; i < count; i++) {\n f[i] = f[i-1] + f[i-2];\n }\n return f;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":56,"value":"md`fibs(${iterations}):`","pinned":false,"hidden":false,"mode":"ojs"},{"id":4,"value":"numbers = fibs(iterations)","pinned":true,"hidden":false,"mode":"ojs"},{"id":34,"value":"stroke = \"steelblue\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"height = 360","pinned":false,"hidden":false,"mode":"ojs"},{"id":36,"value":"steps = {\n const context = DOM.context2d(width, height);\n const marginY = 2;\n context.beginPath();\n context.moveTo(0, height-marginY);\n const stepX = width / iterations;\n const stepY = height / numbers[iterations-1];\n for (let i = 1; i < iterations; ++i) {\n context.lineTo(i * stepX, height - numbers[i-1] * stepY - marginY);\n context.lineTo(i * stepX, height - numbers[i] * stepY - marginY);\n }\n context.lineJoin = context.lineCap = \"round\";\n context.strokeStyle = stroke;\n context.stroke();\n return context.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":137,"value":"fibsAstro = html`

Fibonacci Numbers on Astronomical Scale

\nTo put it in perspective here is a fun math problem:\n

\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":190,"value":"md`**How many Fibonacci Numbers would it take to get us to the Moon?**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":76,"value":"html`\n $\"~1au\"$ \n

\nIf SpaceX developed Fibonacci numbers propulsion engine, how many Fib jumps would it take to reach the Moon?\n

\nAt its closest point, known as perigee, the Moon is only 363,104 km (225,622 miles) away.\nAt its most distant point, apogee, the Moon is 406,696 km (252,088 miles) away from the Earth.\n

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"value":"md`**Answer (in km):**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":87,"value":"fibsToMoon = fibsToNumber(363104)","pinned":true,"hidden":false,"mode":"ojs"},{"id":85,"value":"function fibsToNumber(limit) {\n let f = [0, 1];\n let last = 1;\n let i = 0;\n while (last < limit) {\n last = f[i+2] = f[i] + f[++i];\n }\n return f;\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":159,"value":"html`\n $\"~1au\"$ \n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":103,"value":"md`**to Mars? Range: 54.6 - 225 million km**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"fibsToMars = fibsToNumber(54.6 * 1000000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":130,"value":"md`**to Venus? ~ 108 million km**`","pinned":false,"hidden":false,"mode":"ojs"},{"id":132,"value":"fibsToVenus = fibsToNumber(108 * 1000000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":232,"value":"html`\n $\"Kuiper$ \n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":225,"value":"md`**to [Kuiper belt](https://en.wikipedia.org/wiki/Kuiper_belt)?** \n\nKuiper belt range: **30 - 50 AU** (astronomical units) from the Sun\n\n**1 AU = 150 million km**, avg distance from the Sun to Earth`","pinned":false,"hidden":false,"mode":"ojs"},{"id":234,"value":"fibsToKuiperBelt = fibsToNumber(30 * 150 * 1000000)","pinned":true,"hidden":false,"mode":"ojs"},{"id":113,"value":"fibsNotebooks = html`

Other Fibonacci Numbers Notebooks

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":116,"value":"md`Fibonacci generators: https://beta.observablehq.com/@anglee/fibonacci-generator\n\nFast Fibonacci: https://beta.observablehq.com/@jonathanhawleypeters/fast-fibonacci\n\nGolden ratio: https://beta.observablehq.com/@aaizemberg/golden-ratio`","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}