Thurston proved that a knot must have this property if it is not a torus knot or a satellite knot. A space with this property has as its orientation-preserving isometries the group of real Möbius transformations with determinant one. Spaces with this property have curves called horocycles, can be modeled in two dimensions by Poincaré’s half-plane and disk, and have constant negative curvature. This property is the first word in a class of functions derived from the pair “e-to-the-x plus-or-minus e-to-the-negative-x all over two.” Lobachevsky names a non-Euclidean geometry with this property, which breaks the parallel postulate and has triangles whose angles sum to less than 180 degrees. For 10 points, what property derives from the name of a conic section exemplified by the function one-over-x? ■END■
| Florida | 2025-02-01 | Y | 3 | 100% | 0% | 0% | 99.33 |
| Great Lakes | 2025-02-01 | Y | 6 | 100% | 0% | 17% | 85.50 |
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 83% | 0% | 0% | 88.00 |
| Midwest | 2025-02-01 | Y | 6 | 100% | 0% | 0% | 90.50 |
| North | 2025-02-01 | Y | 3 | 100% | 0% | 0% | 76.67 |
| Northeast | 2025-02-01 | Y | 5 | 100% | 0% | 0% | 73.40 |
| Overflow | 2025-02-01 | Y | 4 | 75% | 0% | 50% | 111.67 |
| Pacific Northwest | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 79.50 |
| South Central | 2025-02-01 | Y | 2 | 100% | 0% | 0% | 80.50 |
| Southeast | 2025-02-01 | Y | 4 | 100% | 0% | 0% | 99.50 |
| UK | 2025-02-01 | Y | 5 | 80% | 0% | 0% | 76.75 |
| Upper Mid-Atlantic | 2025-02-01 | Y | 9 | 100% | 0% | 0% | 78.56 |
| Upstate NY | 2025-02-01 | Y | 3 | 100% | 0% | 0% | 90.33 |
| Player | Team | Opponent | Buzz Position | Value |
|---|---|---|---|---|
| Agnijo Banerjee | Cambridge A | Cambridge C | 47 | 10 |
| Rasheeq Azad | UNC B | William & Mary | 49 | 10 |
| Alex Akridge | Indiana A | WashU B | 55 | 10 |
| Cade Reinberger | RIT A | Cornell D | 57 | 10 |
| Philip Yao | Brown A | Tufts A | 57 | 10 |
| Matthew Westley | Purdue | Iowa | 57 | -5 |
| Conor Thompson | Iowa State | Carleton | 62 | 10 |
| Isaac Mammel | Maryland A | Johns Hopkins A | 62 | 10 |
| Danny Han | Penn A | Rutgers A | 62 | 10 |
| Noah Chen | Columbia B | Yale A | 62 | 10 |
| Luke Robitaille | MIT A | UMass Boston | 62 | 10 |
| Matthew Sumanen | Georgia Tech B | Vanderbilt A | 63 | 10 |
| Henry Bon | Winona State | Minnesota B | 77 | 10 |
| Todd Maslyk | Michigan A | Carnegie Mellon A | 78 | 10 |
| Karan Gurazada | Texas A | TAMU | 78 | 10 |
| Coby Tran | Chicago C | Illinois A | 79 | 10 |
| Ned Tagtmeier | Chicago A | Chicago D | 79 | 10 |
| Chris Levesley | Warwick A | Southampton B | 79 | 10 |
| Michał Gerasimiuk | Stanford B | Northwestern A | 79 | -5 |
| Sophie Higgs | UW A | UBC | 79 | 10 |
| Joel Crossley | Manchester | Imperial A | 80 | 10 |
| Anne Fjeld | Alberta | UW B | 80 | 10 |
| Vedh Ramesh | Penn B | Haverford A | 81 | 10 |
| Joy An | Harvard A | Brandeis B | 82 | 10 |
| Ivan Stanisavljevic | Duke | Liberty A | 82 | 10 |
| Nikhil Nair | BU | Brandeis A | 83 | 10 |
| Aditya Patnaik | Ohio State B | Michigan D | 83 | 10 |
| Richard Niu | Cornell B | NYU A | 83 | 10 |
| William Broker | Haverford B | George Washington A | 83 | 10 |
| Zaid Asif | NYU B | George Washington B | 83 | 10 |
| Jerry Zhang | Harvard B | Dartmouth A | 83 | 10 |
| Stephen Walsh | Northwestern B | Georgetown A | 83 | 10 |
| Bryan Ugaz | ASU | Texas B | 83 | 10 |
| Rohan Dalal | Georgia Tech C | Louisville A | 83 | 10 |
| Bill Zhao | Florida B | UCF C | 84 | 10 |
| Jiping Fang | Illinois C | Missouri | 84 | 10 |
| Mitchell Indek | Michigan B | Michigan State | 84 | 10 |
| Sai Subramanian | Case Western A | Ohio State A | 84 | 10 |
| Patrick Rivas-Giorgi | Columbia C | John Jay College | 84 | 10 |
| Dennis Yang | Michigan C | Carnegie Mellon B | 85 | 10 |
| Leo Law | Florida A | Valencia A | 88 | 10 |
| Alec Riso | Cornell C | Binghamton A | 88 | 10 |
| Chase Woodson | Virginia A | UNC D | 90 | 10 |
| Will Huang | Wisconsin A | Wisconsin B | 91 | 10 |
| Ruchir Kodihalli | Case Western B | Kenyon | 91 | -5 |
| Noah Chin | Virginia Tech A | UNC C | 98 | 10 |
| Ian Switzer | Kenyon | Case Western B | 99 | 10 |
| Adam Iqbal | Durham | Cambridge E | 101 | 10 |
| Sam Macchi | Vassar A | Maryland B | 107 | 10 |
| Liam Starnes | Chicago B | Illinois B | 120 | 10 |
| Miller Doerr | Liberty B | South Carolina | 121 | 10 |
| Juan Landaeta | Florida State A | UCF B | 126 | 10 |
| Collin Nadarajah | WashU A | Indiana B | 126 | 10 |
| Alexandra Knight | Liberty C | Wake Forest | 126 | 0 |
| Adam Pascoe | Wake Forest | Liberty C | 126 | 0 |
| Elliot Cosnett | Oxford B | NYU C | 126 | 0 |
| Jacob Hardin-Bernhardt | NYU C | Oxford B | 126 | 0 |
| Jared Schwartz | RIT B | ESF A | 126 | 10 |
| Patrick Boyle | Notre Dame C | Notre Dame B | 126 | 10 |
| Nikhil Chellam | Northwestern A | Stanford B | 126 | 10 |
| Parker McCoig | Tennessee A | Georgia Tech A | 126 | 0 |
| Tianyu Xu | Georgia Tech A | Tennessee A | 126 | 10 |
| Jack Lewis | Bruin A | Alabama A | 126 | 0 |
| Jackson McDonald | Alabama A | Bruin A | 126 | 10 |