The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger
The Number Devil: A Mathematical Adventure 1. Provide a summary of each chapter. a) Explain the basic premise of each chapter in 5-7 sentences. 2. Create a glossary of terms. a) Define it in your own words. You may use your math book, dictionary, or the internet to help you. Please provide the source used with each term. b) Explain how the term is used in the book. The page numbers for each term can be found in the index. c) Provide your own example to help explain what it means. Arithmetic progressions Continued fraction Diagonals Factorial Fibonacci sequence Golden mean Hexahedron Imaginary numbers Irrational numbers Natural numbers Pascal s Triangle Permutation Pythagorean theorem Square roots Sieve of Eratosthenes Tetrahedron Triangular numbers Vertices Zero power Example: Prime number a number greater than one that is only divisible by itself and one (Math book, p. 128) The number devil calls these prima donna numbers. On the third night, he makes Robert go through many of the numbers to see whether they are divisible by numbers other than just one and itself. Example: 5 is a prime number because its only factors are 5 and 1.
3. Famous Mathmeticians (Twelfth Night) Pick one of the following mathmeticians in the story and explain in two paragraphs what they accomplished that was beneficial to the progression of mathematics. Include what source you used to get your information: Archimedes Georg Cantor Eratosthenes Leonhard Euhler Carl Friedrich Gauss Felix Klein Johan van de Lune Pythagoras Bertrand Russell 4. Choose two of the following activities to include with your mathmetician research, summaries and glossary. Gum in Half & Roman Numerals (First Night) Cut a stick of gum in half. Cut each half in half again. And again. How many times can you halve the halves? Take a picture of the piece of gum each time you cut it in half. Roman Numerals (Second Night) Compare and contrast the use of Roman Numerals and Hindu-Arabic Numerals using a Venn diagram. http://www.educationoasis.com/curriculum/go/go_pdf/compcon_2sherlock.pdf Write the year you were born in Roman Numerals. Was using Roman Numerals easier or more difficult? Why or why not? Explain in one paragraph. Comparing Base 2 and Base 10 (Second Night) Complete the following activity: http://moreofamom.com/wpcontent/uploads/2009/03/comparing-base-two-and-base-ten-systems.pdf Why is 0 so important? (Second Night) In your own words, explain in your journal why zero can never be used in the denominator of a fraction. In other words, why can t you divide by 0? Sieve of Eratosthenes What is a sieve? Explain how the Sieve of Eratosthenes works. Use the following graphic to help you: http://upload.wikimedia.org/wikipedia/commons/8/8c/new_animation_sieve_of_eratosth enes.gif Demonstrate the Sieve of Eratosthenes up to 100 using this worksheet: http://moreofamom.com/wp-content/uploads/2009/02/sieve.pdf Pythagorean Theorem (Fourth Night) Watch this graphic: http://www.davis-inc.com/pythagor/proof2.html How does this prove the Pythagorean Theorem? In other words, explain what is happening.
Triangle Numbers (Fifth Night) Complete the Triangle Number worksheet. Least Common Denominator (Ninth Night) Why do we need the least common denominator? Using pictures and words, explain WHY we need to have a least common denominator to add and subtract fractions. Net (Tenth Night) http://mindflight.plymouth.edu/icet/2002/icet2002/projects/kearsarge/media/pdf/3dfigur e.pdf Take this figure and turn it into a 3D figure. Create another 3D figure (you may choose which one) and its net. Provide both the net and 3D figure separately. Finish the Pattern (Eleventh Night) Explain what is happening in the pattern on p. 221. What happens to the pattern when you extend it to 1, 111, 111, 111 x 1, 111, 111, 111? Due date:
Triangle Numbers Find two or three triangle numbers that add up to the following numbers: 10= 13= 25= 30= 32= 36= 42= 46= 50= 51= 70= 83= 95= 103 =
Here are some wonderful resources for extensions to the project. http://mindflight.plymouth.edu/icet/2002/icet2002/projects/kearsarge/index.html http://www.maa.org/mathhorizons/supplement/mai_devil.htm http://www.museumstuff.com/learn/topics/the_number_devil::sub::summary http://moreofamom.com/the-number-devil/ Answer key for triangle numbers activity: http://moreofamom.com/wp-content/uploads/2009/04/triangle-numbers-answerkey.pdf Answer key to base 2 and 10 activity: http://moreofamom.com/wp-content/uploads/2009/03/practice-writing-inbinary.pdf