9820 research outputs found
Sort by
“Beyond the Stacks” Vol. 6, Issue 2, Spring 2026
No full textIn this Issue: Dean’s Message, pg. 1 Peer Research Consultants, pg.1, 2 Remembering Jonathan Hodge, pg. 2 University Archives Offers Virtual Tour, pg. 3 Photo Spread, pg. 4-5 Student Voices, pg. 6 Faculty Voices, pg. 6 Meet Tolonda, pg. 7 Why I Give…, pg. 8 Librarians Published, pg. 8 Save the Date, pg. 8https://digitalcommons.fairfield.edu/library-newsletter/1012/thumbnail.jp
The 2πe Quantization Rule in exp(iθ): Discovery Through Extreme-Precision Computation
No full textABSTRACT. We report a computational discovery: the Taylor‑series convergence of exp(iθ) exhibits a robust, period‑scaled quantization of term counts converging to 2πe per 2π cycle, realized as an alternating 17–18 term cadence. Using multiprecision arithmetic (up to 4.7×106 decimal digits for 106 periods) and Hull‑spiral visualization, we follow the term‑by‑term phasor sum and identify an “end burst” at the factorial–exponential crossover θn ≈ n!, followed by a double‑exponential collapse of magnitude into a narrow post‑burst regime (the “Planckian abyss”). Unwrapped‑phase analysis reveals discrete phase bands intrinsic to the post‑burst geometry: in an 8‑period window the phase exhibits 26–27 quantized levels with characteristic 2–3 gap alternations, visible across multiple sampling resolutions. These results are reproducible across independent multiprecision implementations and are consistent with resurgence‑style structure in series tails. The refined combination 8*2πe+(7/17+7/18)/2 ≈ 137.03607436, emerging directly from the Hull‑spiral’s geometric constraints, shows striking proximity to 1/α, the fine‑structure constant. We present this as an empirical discovery requiring theoretical explanation; nevertheless, the observed precision indicates a profound connection between the geometry of Taylor series and fundamental constants
“Beyond the Stacks” Vol. 5, Issue 3, Spring/Summer 2025
Full text linkIn this Issue: Drawn to the Library, pg. 1 Drawing People Together, pg. 2https://digitalcommons.fairfield.edu/library-newsletter/1010/thumbnail.jp
To See This Place: Awakening to Our Common Home - wall labels 6x2
Full text linkhttps://digitalcommons.fairfield.edu/commonhome-ephemera/1014/thumbnail.jp
Installation image of the exhibition To See This Place: Awakening to Our Common Home
No full texthttps://digitalcommons.fairfield.edu/commonhome-images/1028/thumbnail.jp
To See This Place: Awakening to Our Common Home - Mattingly Vinyl Panel 18x30
Full text linkhttps://digitalcommons.fairfield.edu/commonhome-ephemera/1000/thumbnail.jp
Dawn & Dusk: Tonalism in Connecticut - Wall Labels 6x4
Full text linkhttps://digitalcommons.fairfield.edu/tonalism-ephemera/1002/thumbnail.jp
Dawn & Dusk: Tonalism in Connecticut- Wall Labels 6x12
Full text linkhttps://digitalcommons.fairfield.edu/tonalism-ephemera/1009/thumbnail.jp