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 |
| Luke Robitaille | MIT A | UMass Boston | 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 |
| Matthew Sumanen | Georgia Tech B | Vanderbilt A | 63 | 10 |
| Henry Bon | Winona State | Minnesota B | 77 | 10 |
| Karan Gurazada | Texas A | TAMU | 78 | 10 |
| Todd Maslyk | Michigan A | Carnegie Mellon A | 78 | 10 |
| Coby Tran | Chicago C | Illinois A | 79 | 10 |
| Ned Tagtmeier | Chicago A | Chicago D | 79 | 10 |
| Michał Gerasimiuk | Stanford B | Northwestern A | 79 | -5 |
| Sophie Higgs | UW A | UBC | 79 | 10 |
| Chris Levesley | Warwick A | Southampton B | 79 | 10 |
| Anne Fjeld | Alberta | UW B | 80 | 10 |
| Joel Crossley | Manchester | Imperial A | 80 | 10 |
| Vedh Ramesh | Penn B | Haverford A | 81 | 10 |
| Ivan Stanisavljevic | Duke | Liberty A | 82 | 10 |
| Joy An | Harvard A | Brandeis B | 82 | 10 |
| Bryan Ugaz | ASU | Texas B | 83 | 10 |
| Rohan Dalal | Georgia Tech C | Louisville A | 83 | 10 |
| Aditya Patnaik | Ohio State B | Michigan D | 83 | 10 |
| Nikhil Nair | BU | Brandeis A | 83 | 10 |
| Jerry Zhang | Harvard B | Dartmouth A | 83 | 10 |
| Stephen Walsh | Northwestern B | Georgetown A | 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 |
| Jiping Fang | Illinois C | Missouri | 84 | 10 |
| Bill Zhao | Florida B | UCF C | 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 |
| Alec Riso | Cornell C | Binghamton A | 88 | 10 |
| Leo Law | Florida A | Valencia A | 88 | 10 |
| Chase Woodson | Virginia A | UNC D | 90 | 10 |
| Ruchir Kodihalli | Case Western B | Kenyon | 91 | -5 |
| Will Huang | Wisconsin A | Wisconsin B | 91 | 10 |
| 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 |
| Alexandra Knight | Liberty C | Wake Forest | 126 | 0 |
| Adam Pascoe | Wake Forest | Liberty C | 126 | 0 |
| Collin Nadarajah | WashU A | Indiana 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 |
| Jared Schwartz | RIT B | ESF A | 126 | 10 |
| Juan Landaeta | Florida State A | UCF B | 126 | 10 |
| Patrick Boyle | Notre Dame C | Notre Dame B | 126 | 10 |
| Jack Lewis | Bruin A | Alabama A | 126 | 0 |
| Jackson McDonald | Alabama A | Bruin A | 126 | 10 |
| Elliot Cosnett | Oxford B | NYU C | 126 | 0 |
| Jacob Hardin-Bernhardt | NYU C | Oxford B | 126 | 0 |