에 의해 게시 Jeff Weeks
1. - The under-appreciated fact that the two traditional models of the hyperbolic plane are simply different views of the same fixed-radius surface in Minkowski space: the Beltrami-Klein model corresponds to a viewpoint at the origin (central projection) while the Poincaré disk model corresponds to a viewpoint one radian further back (stereographic projection).
2. In particular, central projection of the sphere corresponds to the Beltrami-Klein model of the hyperbolic plane, and stereographic projection of the sphere corresponds to the Poincaré disk model of the hyperbolic plane.
3. Most people will want to start with the Torus Games instead, which offer a selection of easily playable games, designed for children ages 10 and up, all implemented in multi-connected spaces in 2 and 3 dimensions.
4. The Hyperbolic Games are similar in spirit to the Torus Games, but played on curved surfaces.
5. The Hyperbolic Games, by contrast, are for math students — advanced undergraduates and beginning graduate students.
6. - The strong — but also under-appreciated — correspondence between the hyperbolic plane and an ordinary sphere.
7. These games are more challenging than the Torus Games because they combine a multi-connected topology with a non-Euclidean geometry.
8. - The hyperbolic plane, as a live scrollable object.
9. Players may pinch-to-zoom to pass from one to the other, or stop to view the model from any other distance.
10. The sudoku puzzles take full advantage of the Klein quartic’s tremendous amount of symmetry.
11. - The Klein quartic surface, viewed with its natural geometry.
또는 아래 가이드를 따라 PC에서 사용하십시오. :
PC 버전 선택:
소프트웨어 설치 요구 사항:
직접 다운로드 가능합니다. 아래 다운로드 :
설치 한 에뮬레이터 애플리케이션을 열고 검색 창을 찾으십시오. 일단 찾았 으면 Hyperbolic Games 검색 막대에서 검색을 누릅니다. 클릭 Hyperbolic Games응용 프로그램 아이콘. 의 창 Hyperbolic Games Play 스토어 또는 앱 스토어의 스토어가 열리면 에뮬레이터 애플리케이션에 스토어가 표시됩니다. Install 버튼을 누르면 iPhone 또는 Android 기기 에서처럼 애플리케이션이 다운로드되기 시작합니다. 이제 우리는 모두 끝났습니다.
"모든 앱 "아이콘이 표시됩니다.
클릭하면 설치된 모든 응용 프로그램이 포함 된 페이지로 이동합니다.
당신은 아이콘을 클릭하십시오. 그것을 클릭하고 응용 프로그램 사용을 시작하십시오.
다운로드 Hyperbolic Games Mac OS의 경우 (Apple)
| 다운로드 | 개발자 | 리뷰 | 평점 |
|---|---|---|---|
| Free Mac OS의 경우 | Jeff Weeks | 7 | 5.00 |
The Hyperbolic Games are similar in spirit to the Torus Games, but played on curved surfaces. Most people will want to start with the Torus Games instead, which offer a selection of easily playable games, designed for children ages 10 and up, all implemented in multi-connected spaces in 2 and 3 dimensions. The Hyperbolic Games, by contrast, are for math students — advanced undergraduates and beginning graduate students. These games are more challenging than the Torus Games because they combine a multi-connected topology with a non-Euclidean geometry. Mathematically they illustrate the following: - The hyperbolic plane, as a live scrollable object. - The under-appreciated fact that the two traditional models of the hyperbolic plane are simply different views of the same fixed-radius surface in Minkowski space: the Beltrami-Klein model corresponds to a viewpoint at the origin (central projection) while the Poincaré disk model corresponds to a viewpoint one radian further back (stereographic projection). Players may pinch-to-zoom to pass from one to the other, or stop to view the model from any other distance. - The strong — but also under-appreciated — correspondence between the hyperbolic plane and an ordinary sphere. In particular, central projection of the sphere corresponds to the Beltrami-Klein model of the hyperbolic plane, and stereographic projection of the sphere corresponds to the Poincaré disk model of the hyperbolic plane. - The Klein quartic surface, viewed with its natural geometry. The sudoku puzzles take full advantage of the Klein quartic’s tremendous amount of symmetry.
PcMac 한국어 
