CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '9134f36e39a6fe0b',cH: 'QFJPZI3isWQpv6Lw8SvrM7Q3.Lw5IqTCTn3V0gPA.xM-1739786641-1.2.1.1-5Nq7h0FIf6L2KUvbSHA04eperkEAz8aPH.Rf2OpBUO.JpTtKqtzeN6x5q6U98dG9',cUPMDTk: "\/abstracts\/search?q=Spiral%20Geometry.&__cf_chl_tk=M7CILAkw9ihMkfe3U3FMguQgwZgPMyjqBkhnZQT9iEA-1739786641-1.0.1.1-_0G6wUs_jxSC9eEzRykTH_H7YDZftA3bq_o7pysWUAw",cFPWv: 'b',cITimeS: '1739786641',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/abstracts\/search?q=Spiral%20Geometry.&__cf_chl_f_tk=M7CILAkw9ihMkfe3U3FMguQgwZgPMyjqBkhnZQT9iEA-1739786641-1.0.1.1-_0G6wUs_jxSC9eEzRykTH_H7YDZftA3bq_o7pysWUAw",md: "vAcm6FVTP6ecAgELe91nfutOCCgSmENBrlIDB8y_kFw-1739786641-1.2.1.1-wtrtGyy6PG9CQM_u4uFlsNOGshI328icDGzdTRj0UG9j7yQs7cX57KJ4Wv.XggOz0QJFfgo70wVrbvZpeLvEtHVlDVsc2Of1tIM.gunLbYZ.khmPuHR7SNIr3v1fpjdmh5PDFi3t1pAQsv5PdhlbCJTlSI3y9PmJ8tdxzjZM8BXe1BCeScxwAhtXGKnp7csPlXzFexu7KueWjJ1bSil0N8jji8tshUM_d7Xk24uRqEAca8.6RGdoSENajY6ajDEHb5TeAlFooQz9XKw6XVAN9t4PznbwimBUVePDMc4OEEe9dB993Lms_j5tKxHubHDyDusdy5BSDzgKmWwA2VlwA9FapUyfhPm1PWQJ1jgD8cOUbuOTw8mSN6FQFl.mpH6gUD1.9aaZw57UKfTDEFA9kpkPQHveSpECy7PrLXfzjKvoKnziUKr6mQFm3coNGXPXaH9ILVJggm1Bh8lesgBE5bwYm1bksB1pVuFdXO5H.Kx4WQd98sQNZ1qYRkfSpa9bNt6diyEkTNjka0uOdXKSN0R3zQg.VhwjbKUxB0yG2Epm7RNbLw5SeHQKwqEfiaxhDJHW.wkWc0cTyIMUR2ut0JjzKPsdrw7qh8v1kkk9Qs2icdkSjsjuA1grRplZp56BHzZEqLIQmVM2h0Edo_F5yKXVTmWe6M6YOMguiBqP89G6v7SD9N8L4gpJcyJzhk50_E_FuZBN4VAfwgq3gQNQ_2oizaCIH052CTESVyJAJh2lGLkCpkdadj4Nmvel4ZQGNVQySJzsXI3hWvIuIjpvAoF4JZSJSkdEajt8BNwxQsuMagW07j3NzV0l8Kzt1N0QA3XwrXI9xXqTnN1_pE8HZcoB297mOQ6OC85AMk57.JQkyjlktBA8q58hJJ9BItisAPPA8ux5XIWX3PC60Gw6ZUA57LB6fuu1lsKHgWyI16g_iyYnp.9awyIy6N_Uu600BpmI8jiJ6epvDOGX4.UN0ObyV598bkP63Zi06EQFG7q9sPrDplnuc9EQ6Sj03sSkPnUbhg1P_wrykVoC86h6bngg0PhJjouOJyKswzdTJFHjKxAF6wczsm6MazQeGAv8ZaREgCklqdyGBs4FoB1RRbq.A9VGUB3wQ3Cgrq2eUa58bss6h0cda8m3npTZ0nSeZtT71_Gn67q0MJHbHhEPxy0ahUApRO5QO4Sh3Xzus4FpHJI4tEwgtMfpTZY4cJWM7Du2bqB_IOWdy15E68GlfylJtEAH.VZIKRetx6eR6sZ4ZLEjaqllNiYDRbBJWuU3pHksEav2nAtaLsbUbKf8HWsXgSBKsTdlB9r6KKjeCuaZPJ6IwJEZxGRfL8KxESMQCTWHdxPykDycSVDpuSfcHv7GeJxj0FQvn665D9Z7d60JG.NBJ5EB.R6lLxmafx4oSCLswQ_XY6lm0GXcF0C0cuCwSeKQRWBRiZbKJItwa3NarRn7LIEZ.19vOaDaUUWETBGApGpJBu0Iln7zaDo3_ornEoMqAxNshCUPPccapE_wluA.KagoBN.xpsGVOBqNN42XPkzBI0fG7xTLZeb97jlhcQdSLBh2gog7Nqtt3ZkS5m.wJDgQFFaTQjSOBZtf1aynLOlNu6A3PYrsiefzSbBogvckuidwndshM2WDn1cvEyL1yQMVhUFEJdwvjuZvl8ni0viJ57iLWVBFdMzwXXobFSTwCUoGyg66uMd50FMve6QcOHKVhFd1mjY5fm5NeYiYnSAgbxg1.nH4IAt8XsJ79_zsxa1_fJr_35gfCORh.YfZgai7y6t1gp0wEr.5gHF7gL83sIKxUlfnOpmB40.elanhdbnaks6STbiyI25j6QMBD9ReaEpU2eMAjPXFowjpD5fIA6w09lOWGKuHI69R21QiMnWat77rsSeHdjiTtGEYA7gJEb8DFyVVpbs5dbBADAcINRVpHPUTrRQLppZS21oCQgUBifTyhwslJjY",mdrd: "YuQpiwq3u8BNX1ocGzq13uAPp38iyInRUzG7nYb_G8s-1739786641-1.2.1.1-SHncSzJFgcXAF85IWcPbHe7LX7bE.DrOno7uH_JTu8bHgZmv3uSjAr1woscQHbYp2aH3qErrKi_tHW3W8KgHIYcfZm_Vie9nxAgXt.PsL6a.Ml4wFkPPwWDfkJeU7IyKWF2j6KLj4HTnIqhSve4ck6OokY8mQuKZtpjhILo0bZ.v2zsjWvEe_T61rtHOBZDl_BJX9w6aXA4NgNkrSSd45iXnBmN7ZGpaA9W88CQIzEqCqter9HVmqbm84_ZhaHOhaCXyoGhw7_xOuLOB82MQOwXCkfO.iyk_PnPjkWJOJou0iwolZ11AKZtY7Sf11yTcmQS.cHcuacgq04MV1z.jYADkAI3Le5El8py3U_NB5fzmu.bvroaLGBE867gP5Ibo_dmAgo2s8ou5x2PmnlLAcR0.dJhMgQKo9.3wmbYfucCWvVZhSq7SdVGgQZPUEb.Wg6.TQB1OKD5Rk79cboRjeSacz0pPL9pb_hhTaA5N92d49SPzE.Y0ia47Aru8fiDn5QmV8Kygn6rrG_JHblexZjZwAil_PUEU7WLB2Gh2b3r8WS_OA6MupECo4UFx.FS6waD6sarMtml3RBIbQsr0Z9P.iaP0SYn5Mbw1gnuIXSXptcLZTW_g5zGoQ3ABQbMpCgdtTUg.ZhSKVN6HDRebjjl1XNxJ.PfcmUqiiuLrxitiSVoKdSoBo3i0z4K_wGr0GaYnxliJ4GwjOmDdzTCNx83.oVeQ1br2JXb8rdDl8XoWzYlvC7gb9a3mIc2Q9rO_3Oq2kDUSubqJYC1JPnhOr8OmgR.lhY0Ebam3LjfJ9mlV3pb2f4wg7Q2W0TxNW1rRpIFJsVaQJfw.M0uqpDfAp0.z4RncWUAOyKgQSOdQvbZRwnN3X_qq7H7CW0jaewvylpv4EdE9XFM4ZmXgO95OYl7i1RAJbV5EH0gLj1cr5f9TTACce5xKZCGVclqnADRtniaI8wEbUt6jDdR2Bio1Vv5M3csfU4aRjWwM9Yfbg5WKQRI9TmsyBr4YTGvWcKDRYxk8xvX4mYcYmrAAaT4z5fdBwXEgv8KoLTb.hVbJWQZvDyce8VibG1olLPI1HlEfC1nDHldvySzaoR8r0ntiGVRTxXSnaKLTIcKBfLrYhjbc4XJZrxlB1eq14rLIz_Qiz6dQtMZPWL7WEt00SUe9CeLeQJ2c3khm.mr0iLhDAJk68wg.qwD38f8M7A79BMvcOywOJ2qo.3n8LWYUt_.bC43Qp_C8Bd67e2BKBbHueuNVBVktSkzS76vc5A8di333twK0o8hjNy8BMhXicn6TTVDG4xpB2V5pZ9abQQU3pvqvUc6HiZtBw6OoyDlOhLGgXEw05DAuBlPTHyIzZkgVgBNikQ5xG1wM0FTtv4A4HokjNK5A8dHX5nqffVcgSqKiNtqy9klvhqSfnY3EaG0E.va2t5mpEgBHBTh9L83mzNKCpZ62LS9LwNyyk0YXyd76ed9LUvNBtm6sY4RxShElJcV8EveWPU0kzzTmduJQAGuAiNKTAnJI5uu.keerp9HlkN0G72DSY2bDnr9v9p4Mbvtlmm0qOrO2hAPgUyzuVhuu.3sKsmw5B5H6Zk48l2ZD_NiYetUYjMJPjBle9jcFWLedyPdiK3dq_hmHwSyaf1uy1bBgtzPGu11AtIAf6OAp7fim85XH4naARwmzUzU4qE6DAQaG3fD_3YMInOCtP7IK2nosaJm.pr8ApvcP2RJ6.Ie3t44W5JGUcUBOEVvjqZsVFuaswQLLyAkqlW_nDlOWCrcMsHc3PphMOd_FquBclcrpY71FlCTkfMWjo067jelej5JFjyDV8YUQ6vK.viU41ZD9tv1QzTFmvYbSaSpbbYWLP0T08PW4hyJSipylWxkGt6spXSaupxP0LkL_CK7yu.BGyNAd5_u9LupMluVF4toPpvNZZnoovJi0PBdJ3qXgDG_T4M1wCcfLjZUXq03FSRaoN1A7a1GTWU1KmDJJ"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=9134f36e39a6fe0b';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/abstracts\/search?q=Spiral%20Geometry.&__cf_chl_rt_tk=M7CILAkw9ihMkfe3U3FMguQgwZgPMyjqBkhnZQT9iEA-1739786641-1.0.1.1-_0G6wUs_jxSC9eEzRykTH_H7YDZftA3bq_o7pysWUAw" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>