Harmonic Mathematics

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Download a Geometry Expressions Model for Harmonic Mathematics

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Symbolic computations on this page use the GeoGebra CAS engine.

  
 

   
 

Introduction

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What Do You Mean?

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Calculate the Means

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Harmony, Music and Mathematics

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Pictures of Harmony

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Constructing the Means

Pappus 320AD

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diameter
x
0 0.50 2


 

 

App generated by Geometry Expressions

 

When x = 0.50 and diameter - x = 1.50 then:

Arithmetic Mean = 1.000

Geometric Mean = 0.863 and

Harmonic Mean = 0.745


 

 

Use the MathBox above to enter a function for graphing, table of values OR expressions for CAS: Define functions, simplify expressions, solve equations...
For example, enter Solve(x^2-x-1=0) and press the CAS button. More?

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Listen to your Function?

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Assessment

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Symbolic computations on this page use the GeoGebra CAS engine.


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