Pythagorean Quilt

The world of mathematics beckons a challenge to all of us to discover its hidden wonders. This mathematical quilt is composed of four right triangles, each of which is surrounded be three squares, and which exhibits Pythagoras’ famous theorem: a2 + b2 = c2. Other mathematical treasures displayed within this quilt include: geometric shapes, algebraic symbolism, famous constants, prime numbers, and various mathematical concepts.

Such mathematical challenges are part of all our mathematics courses offered at Chi Hi but are particularly emphasized for our Math Investigations courses.

The Dragon Face

The ancient Greeks introduced many construction problems that were to be solved using only a straightedge and compass. These limitations still apply to many constructions that are part of today’s geometry courses.

One half of the dragon face is created by placing the center of a compass at various locations on a Cartesian coordinate grid and striking designated arcs. The other symmetrical half of the face is completed by reflecting all the arcs across a vertical line of symmetry.

These geometric concepts are applied not only in Chi Hi’s Geometry courses, but are also used to stimulate student interest in our Survey of Math and Living Mathematically courses.

Mathematical Snowflake

Every snowflake has an infinite beauty that is crafted through the skill and artistry of Mother Nature. Likewise, students can produce their own unique paper snowflakes by the use of creative imaginations and mathematical concepts.

Our snowflake displays rotational symmetry, symmetry of certain alphabet letters, mathematical symbols and shapes, and the creativity of an advanced student at Chi Hi to create a truly mathematical snowflake. Other paper snowflakes can be seen displayed in some of the math classrooms during the cold winter months.

Navajo Rug

The Navajo Indians of the Southwestern United States are well known for their intricate and beautiful rug creations. Several mathematical concepts, especially the use of Fibonacci numbers, play an integral role in the design of many of these rug patterns.

Students in Chi Hi’s Survey of Math courses are asked to use their imaginations to create their own Navajo rug designs by symmetrically placing 3-step, 5-step, 8-step, and 13-step “cut-outs” of various colors on poster board.

The Mandelbrot Set

The Mandelbrot Set consists of points in the complex plane that are bounded when undergoing an infinitely iterative (repeated) process which involves simple algebraic operations.

It is the elaborate boundary of this set that forms a fractal that does not simplify at any magnification. The Mandelbrot Set has been popularized for its aesthetic appeal and for its complexity that arises from its simple definition.

The Mandelbrot Set is introduced to Chi Hi students in Algebra II classes and examined further in our Math Investigations, Intro Calculus, and AP Calculus courses.

Sierpinski’s Triangle

If line segments are drawn between each pair of midpoints of the sides of an equilateral triangle, four smaller congruent triangles are formed. If the middle triangle is removed, the resulting figure represents the first stage in creating Sierpinski’s triangle. If this process is repeated for the three remaining triangles, the second stage for Sierpinski’s triangle is completed. If this process is continued indefinitely, Sierpinski’s triangle is created.

Paradoxically, the area of Sierpinski’s triangle is zero, but the total length of the line segments that form all of the triangles is infinite.

In Chi Hi’s Math Investigations course, students explore these geometric concepts along with other mathematical procedures that create Sierpinski’s triangle.

Cryptology Ribbon

Cryptology techniques can be very simple or very complex and nearly always involve mathematics. One technique used by the Spartan government 2500 years ago is illustrated by the encoded message that is partially displayed by the ribbon on the wall.

Your challenge is to identify the hidden letters of the encoded message on the wall whose original text was Albert Einstein’s famous saying:

Pure mathematics is,
in its own way,
the poetry of logical ideas.

Similar cryptology challenges are offered in Chi Hi’s Survey of Math, Algebra II, Math Investigations, and AP Calculus class

Lizard Tessellation

The lizard tessellation by M. C. Escher consists of interlocking figures that repeat over a flat surface without any gaps or overlaps. This drawing and other tessellating shapes are created through specific geometric translations and rotations.

However, such tessellations involve more than just mathematical techniques. It is the human imagination that interprets and gives meaning and beauty to contour lines that create these fascinating tessellations.

Tessellations are discussed in Chi Hi’s Geometry classes while students in Survey of Math, Living Mathematically, and Math Investigations are given the opportunity to create their own tessellations.

Graphing Calculator

No other recent innovation has changed the scope and direction of mathematics education as mush as that of the graphing calculator.  This powerful technology has enabled students and teachers to investigate a wide array of mathematical relations and delve deeper into mathematics than previously possible.

Graphing calculators are required for Chi Hi students enrolled in Algebra II, Probability & Statistics, Math Investigations, Intro Calculus, and AP Calculus