13.7.2: Key Concepts
- Page ID
- 129694
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
Key Concepts
13.1 Math and Art
- The golden ratio, ϕ, can be found in nature, and the relationship is often associated with beauty and balance.
- The Fibonacci sequence reflects a pattern of numbers that can be found in various places in nature. The sequence can be used to predict other values that follow the Fibonacci pattern.
- State some naturally occurring applications of the Fibonacci sequence.
- State some naturally occurring applications of the golden ratio.
- Determine if a rectangle is golden.
- State some artistic applications of the golden rectangle.
13.2 Math and the Environment
- Recognize how water conservation by one person, family, community, or nation can positively impact the world’s freshwater supply.
- Recall components from the history of solar use by mankind.
- Calculate electrical demand given watts.
- Recognize advantages of residential solar power.
13.3 Math and Medicine
- Compute volumes of prescription drugs in liquid and pill form.
- Validate the effectiveness of a new drug.
- Mathematical modeling can be used to describe and track the spread of a virus.
13.4 Math and Music
- As frequency of a sound increases, the pitch of the sound increases.
- Hertz is a unit of measurement for frequency.
- Decibel is a unit of measurement for the intensity of sound.
- Half-steps and whole-steps describe one type of movement between two notes on a keyboard.
- Octaves are a collection of any 12 consecutive notes, which is a foundation in music theory.
13.5 Math and Sports
- Describe how a round-robin tournament is organized.
- Compute the number of games played in a round-robin tournament.
- Describe how a single-elimination tournament is organized.
- Compute the number of games played in a single-elimination tournament.