上面照片中高耸的结构是阿莱格尼-石灰岩之间非凡合作的结果, 欣斯代尔, Olean, and Portville school districts called Connect 4项目. 13英尺高, 32,由87名中学生使用名为Zometool的建筑系统建造了770块结构. 数学上，这个结构代表了一个美丽的几何图形，叫做a stage-6 Sierpinski四面体 (or 6级tetrix). Connect 4项目 was organized by Dr. 克里斯。希尔. The project was generously supported by Cattaraugus-Allegany BOCES.
How was the structure made?
In each of the four districts, 一组学生在老师的指导下搭建了一个阶段5的Sierpinski四面体, which stands over six feet tall and contains 8,194个Zometool组件. 每个老师或一组老师都设计了一个时间表来建立他们的第五阶段结构，这对他们的学生来说是最有效的, 一些小组在2014年秋季完成了他们的部分，其他小组在2015年春季完成了他们的部分. Linda Dodd-Nagel worked with 19 eighth-graders at Allegany-Limestone Central School; Holly Edwards and Matthew Taub worked with 36 fifth-graders at 欣斯代尔中心学校; Jake Palo, Christine Armstrong-Gabler, 莫林Ullman, and Katie Ralston worked with 18 students at Olean Intermediate Middle School; and Bill Torrey and Matt Burlingame worked with 14 seventh- and eighth-graders at Portville Central School.
许多学生, 老师, and administrators involved in the project were present at the grand finale, which was held on May 7, 2015 in the Quick Center for the 艺术' Rigas Family Theater. 最后，四个5级结构被连接成一个6级Sierpinski四面体. 与 theme music to "2001: A Space Odyssey" 在舞台上演奏, 一群老师轻轻地把一个阶段5放在其他三个阶段的顶部，以完成最终的结构. 和... 结构保持不变! The following video captures the completion of the Connect 4 Project.
After the world premier at the Quick Center, the Zometool stage-6 Sierpinski四面体 went on tour, spending time at Olean Intermediate Middle School, Allegany-Limestone Central School (for their 艺术 Festival), 欣斯代尔中心学校 (for their Spring Concert), Portville Central School, and finally the Olean Center Mall.
Is this some kind of record?
我们相信是这样! In a congratulatory letter to the students and 老师, the Chief Visionary Officer of Zometool, 保罗Hildebrandt, 表示,, 据他所知, 这是第一次使用Zometool构建6级Sierpinski四面体. Zometool President Carlos Neumann featured the project on the company’s 主要的网站 还有facebook页面.
为什么“连接4”?
这些努力, which spanned two years from conception to completion, was called Connect 4项目 for two reasons. 第一个, the four school districts involved are those in the Connect 4 Program, which facilitates the sharing of resources among the four districts. 其次，将4个5级结构从字面上连接起来形成6级结构.
这些是学生!
世界上第一个用Zometool制作的6级Sierpinski四面体是由来自Allegany-Limestone Central school的87名中学生制作的, 欣斯代尔中心学校, Olean Intermediate Middle School, and Portville Central School. 在以下照片中, 每组学生与完成的第五阶段结构或在自己学校的第五阶段结构一起摆姿势.
The Allegany-Limestone group, guided by Linda Dodd-Nagel.
欣斯代尔组(由两个班组成)，由霍利·爱德华兹和马修·陶布指导..
The Olean group, guided by Jake Palo, Christine Armstrong-Gabler,
莫林Ullman, and Katie Ralston.
The Portville group, guided by Bill Torrey and Matt Burlingame.
More photos from the finale
One student from each school was selected to represent their group in a
special photographic memento of the occasion, as seen above and in the
下面的特写. Go Bobcats, Huskies, Panthers, and Gators!
With powerful theater spotlights illuminating the structure from
above, the Sierpinski四面体 practically glows.
In the image above, the theater lights were off and a flash, placed
behind the structure, was triggered at the instant the photo was
采取. Check out the cool shadow on the floor.
与 flash in front of the structure and a white screen behind,
we got another awesome shadow.
Dr. 克里斯。希尔 hangs out within a stage-6 Sierpinski四面体.
里面的天气是
真的 不错的.
What is a stage-6 Sierpinski四面体 & Zometool是什么?
A Sierpinski四面体 or tetrix is a certain geometric figure. 它的形状是由四个更小的四面体组成的四面体, each of which is comprised of four even smaller tetrahedra, each of which is comprised of four even smaller tetrahedra, 等等......, 无限. A Sierpinski四面体 is an example of a 分形. The figure is named for the Polish mathematician Wacław Sierpiń滑雪, who studied the two-dimensional analogue called a Sierpinski三角形.
一个Sierpinski四面体包含无限多的小四面体的“层”. 由于Sierpinski四面体包含了无限多的细节，因此无法在物理上构建. However, approximate models of a Sierpinski四面体 can be built. 近似模型的“阶段”表示模型中较小四面体的层数. 0阶段的谢尔宾斯基四面体只是一个四面体——它不包含更小的四面体. A stage-6 Sierpinski四面体 contains six “levels” of smaller tetrahedra. 右图显示的是乔治·哈特3d打印的第5阶段西尔宾斯基四面体模型.
Zometool 是数学上精确的建筑几何结构的塑性构造系统吗, from simple polygons to “shadows” of four-dimensional figures, from models of DNA molecules to works of art.
Technical details, including the parts count
一个特定阶段的Sierpinski四面体的Zometool模型可以使用连接球和 要么 red struts and blue struts or 绿色struts. 我们选择使用红色和蓝色使结构在视觉上更有趣. 此外，由于连接球是白色的，红色和蓝色的支柱构成了一个爱国项目! 使用红色支柱和蓝色支柱(而不是绿色支柱)的一个缺点是，红色支柱和蓝色支柱的长度不完全相同(尽管它们很接近)。, so the resulting tetrahedra are not regular (although they're close). The photo to the left shows, 从左到右, 一个0阶段, 一个阶段1, and a stage-2 Sierpinski四面体 made from Zometool.
通过制作四个Sierpinski四面体的特定阶段的副本并将它们连接成四面体的排列, you build the next stage of a Sierpinski四面体. 出于这个原因, 第6阶段的Sierpinski四面体非常适合由四组学生组成的项目.
一个Zometool stage-6 Sierpinski四面体，有红色和蓝色支柱，需要8194个球, 12288 R1s, 12288个b1, for a total of 32770 parts. 一般来说，对于任意正整数n，一个Zometool stage-n Sierpinski四面体需要2(4)n) + 2个球，3(4)n) r1和3(4)n) B1s, for a total of 8(4n) + 2个部件.
感激之情
Connect 4项目得到了cataraugus - alleany BOCES的慷慨支持.
The project would not have been possible without the support and guidance of the administrators from the four districts: Superintendent Karen Geelan of the Allegany-Limestone School District; Principal Cory Pecorella of Allegany-Limestone Middle School; Superintendent Larry Ljungberg of the 欣斯代尔 School District; Principal Laurie Cuddy of 欣斯代尔中心学校; Superintendent Colleen Taggerty of the Olean School District;
Principals Joel Whitcher (grades 4, 5), Gerald Trietley (grades 6, 7), and Barbara Lias (grades 8-12) of Olean Intermediate Middle School and High School; Superintendent Tom Simon of the Portville School District; and Principal Larry Welty of Portville Central School.
路德维希·布伦纳, Executive Director of the Quick Center for the 艺术, provided the Rigas Family Theater, which was the perfect venue for the finale. 草木不, Technical Director of the Quick Center, gave us indispensable assistance in staging the finale.
奥利恩学区中央接待处的克拉拉·怀尔德(Clara Wilder)在参观的每一站都运送了这座建筑, which made the tour possible.
了解更多信息
For more about mathematics outreach at St. Bonaventure, please contact Dr. 克里斯。希尔. To learn more about Zometool, see Dr. 希尔的网页 Zometool资源.