In ancient Greece, a young musician makes exciting discoveries. The boy Pythagoras, brimming with curiousity, steps up to help when his friend Octavius might be unable to compete in an upcoming musical contest. The problem is an awful noise coming from Octavius's new pipes. With a stylus, clay tablet, measuring cord and his sharp wits, mathematician-to-be Pythagoras figures out the relationship between pipe length and resultant sound and helps fashion a perfectly pitched set of pipes for Octavius. The lyres of his friends Amara and Reyna provide a more difficult challenge, one that Pythagoras solves (in a race against the clock) with scales and tiny rocks. He does it so successfully that he and his friends form Pythagoras and the Ratios...the first rock group! The book's educational aspects are fascinating--both the text and the acrylic-and-colored-pencil illustrations bring these to life--but it's flat-footed on the story's narrative aspects, both visually and textually. Helpful addenda provide interesting information on Pythagoras and the application of his ratios to music.

This picture-book introduction to ratio and proportion also explains the connection between math and music through a story featuring young Pythagoras and his family. Preoccupied by mathematical problems, the protagonist is constantly in trouble with his parents for neglecting his chores. When his cousin Octavius offends everyone's ears with the dissonant pipes he is practicing for an upcoming music contest, the young mathematician hears a challenge. He measures his own set of melodious pipes, calculating the ratio of each pipe to the shortest one, and discovers that Octavius's pipes need to be shortened. Later, he tunes other cousins' lyres by attaching rocks to the strings to adjust the tension. With all the instruments finally ready, the cousins play together at the contest. Unfinished chores and a broken set of pipes leave Pythagoras out of the performance, but the end result is the first "rock" group, which is a big success. The story is amusing and offers a glimpse into life in ancient Greece. Acrylic and colored pencil cartoons depict the clothing and lifestyle of the period in a pleasing palette. A historical note and an experiment in which readers are challenged to use Pythagorean ratios to create a musical instrument with six glasses of water in varying amounts are appended.

Young Pythagorus is curious about the terrible noise coming from his cousin's new pipes. By measuring the length and width of each of the pipes, Pythagorus figures out how "the relationship among my pipes is what makes them sound good together." Pythagorus keeps exploring relationships among all kinds of things. A Historical Note and instructions on how to make an instrument using Pythagorean ratios and how to tune modern instruments offer some good possibilities for the classroom.

In this entertaining story, a young Pythagoras is so focused on helping his cousins and friends with their musical instruments that he forgets his chores. When his friend complains of the terrible sounds coming from his musical pipes, Pythagoras is able to determine that the sound is based on the lengths of the pipes, and that by adjusting the lengths, the sound improves. Historically, Pythagoras was the first person to define acoustic relationships between strings of proportional lengths, so hidden in this simple story is a clear explanation of Pythagorean ratios that any child will find easy to understand. The text is clear, and acrylic and colored pencil illustrations liven up the story. The final page of the book provided a historical note on Pythagoras and the application of mathematics to music. The author also includes an experiment for readers to create their own musical instruments using six glasses of water. This is the second collaboration from Ellis and Peacock on a math adventure, with the first being What's Your Angle, Pythagorus?

Pythagoras and the Ratios is a "math adventure" book appropriate for younger readers who are just beginning to learn about measurements. Easy to understand language introduces a potentially confusing topic for young learners. "We can simplify these numbers, if we divide both the top and bottom numbers by the greatest common factor. For 24 over 12, I can divide both by 12." When this statement is made, the neighboring page has a comparison chart of the two measurements Pythagoras is making to help readers understand. This book is based off the man behind the Pythagorean Theorem. Pythagoras and the ratios depicts the ancient Greek people fairly well, showing traditional dress and instruments accurately.