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 |
| Philip Yao | Brown A | Tufts A | 57 | 10 |
| Cade Reinberger | RIT A | Cornell D | 57 | 10 |
| Matthew Westley | Purdue | Iowa | 57 | -5 |
| Luke Robitaille | MIT A | UMass Boston | 62 | 10 |
| Danny Han | Penn A | Rutgers A | 62 | 10 |
| Noah Chen | Columbia B | Yale A | 62 | 10 |
| Conor Thompson | Iowa State | Carleton | 62 | 10 |
| Isaac Mammel | Maryland A | Johns Hopkins A | 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 |
| Michał Gerasimiuk | Stanford B | Northwestern A | 79 | -5 |
| Sophie Higgs | UW A | UBC | 79 | 10 |
| Chris Levesley | Warwick A | Southampton B | 79 | 10 |
| Coby Tran | Chicago C | Illinois A | 79 | 10 |
| Ned Tagtmeier | Chicago A | Chicago D | 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 |
| Jerry Zhang | Harvard B | Dartmouth A | 83 | 10 |
| Rohan Dalal | Georgia Tech C | Louisville A | 83 | 10 |
| Richard Niu | Cornell B | NYU A | 83 | 10 |
| Aditya Patnaik | Ohio State B | Michigan D | 83 | 10 |
| Nikhil Nair | BU | Brandeis A | 83 | 10 |
| Stephen Walsh | Northwestern B | Georgetown A | 83 | 10 |
| Bryan Ugaz | ASU | Texas B | 83 | 10 |
| William Broker | Haverford B | George Washington A | 83 | 10 |
| Zaid Asif | NYU B | George Washington B | 83 | 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 |
| Jiping Fang | Illinois C | Missouri | 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 |
| 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 |
| Juan Landaeta | Florida State A | UCF 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 |
| Collin Nadarajah | WashU A | Indiana B | 126 | 10 |
| Jared Schwartz | RIT B | ESF A | 126 | 10 |
| Alexandra Knight | Liberty C | Wake Forest | 126 | 0 |
| Adam Pascoe | Wake Forest | Liberty C | 126 | 0 |
| 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 |