What a Math Book

rmys94, Nov 7, 2017

[b]Description of the book[/b][color=#c51414][/color]

Table of Contents

  1. What the book is about..
    1. Four color challenge
  2. 2. The Secret World of Circles
    1. Circle Area (By Peeling!)
    2. Radians in Unit Circle
    3. Circumference of a Circle
  3. 3. Family tree of Quadrilaterals
    1. Cyclic Quadrilaterals
    2. Finsler-Hadwiger Action!!!
    3. Rhombus Action + Sequel = GoGeometry Action 7!

1.

What the book is about..

This book's aim is to practice math concepts while having fun with it.

  • 1. Four color challenge

1.1.

Four color challenge

Instructions:
Complete the coloring of this map, so that no two adjacent regions are the same color. You can only use four colors: [color=#3d85c6]Blue[/color], [color=#6aa84f]Green[/color], [color=#ff0000]Red[/color], and [color=#8e7cc3]Purple[/color].[br][br]Click on the regions (quadrilaterals) to color them. To change the color, click again on the same region.
This puzzle has many solutions. You can see one here: [url=https://4.bp.blogspot.com/-Wtvv_5pkIHk/WE4_Ho9EasI/AAAAAAAALDs/FZn7OE_hSG0uFfWPvRO9eHD6_OcH1dH6gCLcB/s1600/sol1.png]A solution[/url]
Updated version using [url=https://www.geogebra.org/material/show/id/pGCXX3wW]Coloreando el mapa[/url] by [url=https://www.geogebra.org/ilarrosa]Ignacio Larrosa Cañestro[/url]
– Juan Carlos Ponce Campuzano

2.

2. The Secret World of Circles

What do you think about circles? Do they look like a magical shape? Why are they so special?

  • 1. Circle Area (By Peeling!)
  • 2. Radians in Unit Circle
  • 3. Circumference of a Circle

2.1.

Circle Area (By Peeling!)

[b][color=#c51414]Questions for Extension and Application:[/color][/b][br][br][color=#1551b5]1) Was the "triangle" formed truly a triangle? Explain why or why not. [br][/color][br][color=#1551b5]2) What would we need to do to the number of "peels" in order to make the so-called "triangle" formed look[br] more smooth (like a true triangle) vs. a "choppy" triangle? [/color][br][br][color=#1551b5]3) Suppose an above-the-ground circular swimming pool has a radius of 12 feet. What is the area of the exposed surface of the water it contains? [br][br]4) Suppose a circular track (that surrounds grass) has a circumference of 500 feet. If 3 bags of grass seed are needed to be spread out across every 100 square feet of grass in the circular region inside this track, determine how many entire bags of grass seed will be needed to cover the entire area of the circular region surrounded by this track. [br][br]5) Suppose a 12-inch pizza (pizza with diameter = 12 inches) costs $12.00. Suppose a 24-inch pizza costs $24.00. Which pizza is the better buy? Explain why this pizza is the better buy. (Assume both pizzas have the same thickness.) [br][/color]
– Tim Brzezinski

2.2.

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2.3.

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3.

3. Family tree of Quadrilaterals

What are the relationship between quadrilaterals? Are they a family? We guess so.. What makes them a family?

  • 1. Cyclic Quadrilaterals
  • 2. Finsler-Hadwiger Action!!!
  • 3. Rhombus Action + Sequel = GoGeometry Action 7!

3.1.

Cyclic Quadrilaterals

[color=#ff0000][b]Definition:[/b][/color][br][br]A [color=#0000ff][b]cyclic quadrilateral[/b][/color], by definition, is [color=#0000ff]any quadrilateral that can be inscribed inside a circle.  That is, all 4 vertices of a cyclic quadrilateral always lie on the circle itself. [/color] [br][br]Mess around with the applet for a couple of minutes, and then answer the questions that follow.  [br]
Based upon your observations, [color=#ff0000][i]what can you conclude about both pairs of opposite angles of any cyclic quadrilateral?[/i][/color]  [br][br]Prove your assertion true using a theorem previously learned.  Explain fully why what you've observed in the applet above is true.   [br][br]
– GeoGebra Team German, Tim Brzezinski

3.2.

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3.3.

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