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Chapter 7 Review Exercises

Chapter 7 Review Exercises
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  • 23. DNA

    Deoxyribonucleic acid (DNA) is the genetic material in all known living organisms and some viruses. DNA contains two strands wrapped around each other in a double helix. Use the Internet to describe how the Fibonacci sequence is related to each full cycle of a DNA double helix.

    • Worked-Out Solution

      The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21 are numbers in the Fibonacci sequence. Their ratio (about 1.62) is close to the golden ratio.

      The angstrom is a unit of length equal to 1 x 10-10 meter. Even though the angstrom is not formally part of the International System of Units, it is often used in technology and science to express the size of atoms, wavelengths of light, and integrated circuit parts.

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     _____      ______    _  __     ___      _____   
    |  __ \\   /_   _//  | |/ //   / _ \\   /  ___|| 
    | |  \ ||   -| ||-   | ' //   / //\ \\ | // __   
    | |__/ ||   _| ||_   | . \\  |  ___  ||| \\_\ || 
    |_____//   /_____//  |_|\_\\ |_||  |_|| \____//  
     -----`    `-----`   `-` --` `-`   `-`   `---`   
                                                     
    
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  • 24. DNA

    Deoxyribonucleic acid (DNA) is the genetic material in all known living organisms and some viruses. DNA contains two strands wrapped around each other in a double helix. Use the internet to determine whether the golden ratio applies to a DNA double helix.

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      _____      ___                 ___      _  _   
     / ____||   / _ \\      ___     / _ \\   | \| || 
    / //---`'  / //\ \\    /   ||  / //\ \\  |  ' || 
    \ \\___   |  ___  ||  | [] || |  ___  || | .  || 
     \_____|| |_||  |_||   \__ || |_||  |_|| |_|\_|| 
      `----`  `-`   `-`     -|_|| `-`   `-`  `-` -`  
                             `-`                     
    
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  • 25. B-form DNA

    In B-form DNA, the intertwined strands make two grooves of different widths, referred to as the major groove and the minor groove. Use the Internet to describe how the Fibonacci sequence is related to the major and minor grooves of B-form DNA.

    • Worked-Out Solution

      The major groove has a length of 21 angstroms. The minor grove has a length of 13 angstroms. 21 and 13 are numbers in the Fionacci sequence. Their ratio is close to the golden ratio.

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     _____      ______   _    _      ___     ______   
    |  __ \\   /_   _// | |  | ||   / _ \\  |      \\ 
    | |  \ ||   -| ||-  | |/\| ||  / //\ \\ |  --  // 
    | |__/ ||   _| ||_  |  /\  || |  ___  |||  --  \\ 
    |_____//   /_____// |_// \_|| |_||  |_|||______// 
     -----`    `-----`  `-`   `-` `-`   `-` `------`  
                                                      
    
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  • 26. B-Form DNA

    In B-form DNA, the intertwined strands make two grooves of different widths, referred to as the major groove and the minor groove. Determine whether the golden ratio applies to B-form DNA.

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     _    _    _    _    __   _     ______    ____    
    | |  | || | || | || | || | ||  /_   _//  |  _ \\  
    | |/\| || | || | || | '--' ||   -| ||-   | |_| || 
    |  /\  || | \\_/ || | .--. ||   _| ||_   | .  //  
    |_// \_||  \____//  |_|| |_||  /_____//  |_|\_\\  
    `-`   `-`   `---`   `-`  `-`   `-----`   `-` --`  
                                                      
    
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  • 27. DNA Cross-section

    Use the cross-sectional view of a DNA double helix shown. Show how two pentagons can be used to construct the cross-sectional view of a DNA double helix.

    • Worked-Out Solution

      By placing two pentagons together and then rotating one of them, you have the shape of the cross section of a DNA double helix.

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      _  __   __   __    _____    _    _     _____   
     | |/ //  \ \\/ //  |__  //  | || | ||  /  ___|| 
     | ' //    \ ` //     / //   | || | || | // __   
     | . \\     | ||     / //__  | \\_/ || | \\_\ || 
     |_|\_\\    |_||    /_____||  \____//   \____//  
     `-` --`    `-`'    `-----`    `---`     `---`   
                                                     
    
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  • 28. DNA Cross-section

    Use the cross-sectional view of a DNA double helix shown. How is the cross-sectional view of a DNA double helix related to the golden ratio?

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                 ___      ____      _____             
        ___     / _ \\   |  _ \\   |  ___||     ___   
       /   ||  / //\ \\  | |_| ||  | ||__      /   || 
      | [] || |  ___  || | .  //   | ||__     | [] || 
       \__ || |_||  |_|| |_|\_\\   |_____||    \__ || 
        -|_|| `-`   `-`  `-` --`   `-----`      -|_|| 
         `-`                                     `-`  
    
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