# Difference between revisions of "The Right Triangle and the Pyramids Exploration"

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Jump to navigationJump to search (New page: 1. Below are some Pythagorean triples. Compute the seqed - in this case b/a - in each case. {| border="1" |- ! Triple (a, b, c) !! Corner Angle !! Seqed (b/a) |- | ( 3, 4, 5) || <math>...) |
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+ | 1. For the following pyramids compute the Seqed if possible. <br> | ||

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− | ! | + | ! Pyramid !! Height !! base !! Seqed of the pyramid !! Slope !! Possible right triangle |

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− | | ( | + | | Great Pyramid (Khufu) || 146.6 || 230.3 || || 51.8 degrees || |

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− | | | + | | Khafre || 143.5 || 215.25 || .75 || 53.1 degrees || 3-4-5 Triangle |

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− | | | + | | Menkaure || 66.45 || 103.4 || .79 || 51.3 degrees || Maybe 3-4-5 Triangle? |

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− | | | + | | Userkaf || 49 || 73.3 || || 53 degrees || |

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− | | | + | | Sahure || 48 || 78.5 || || 50.5 degrees || |

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− | | | + | | Queen Khentkawes || 72 || 25 || || 52 degrees || |

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− | | | + | | Djedkare || 52.5 || 78.75 || || 52 degrees || |

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− | | | + | | Djedkare's Queen || 21 || 41 || || ca 45 degrees || |

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− | | | + | | Teti || 52.5 || 78.5 || || 53.1 degrees || |

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− | | ( | + | | Teti's Queen (Iput) || 21 || 21 || || 63 degrees || |

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− | + | 3. Note the interesting difference between the pyramids of the Kings and those of the Queens. It is quite common for the Queens to have a much smaller pyramid. | |

− | + | The volume of a pyramid is given by <math>1/3 b^2 h</math>. <br> | |

− | + | (i) Compute the volume the pyramids of Kings like Djedkare and Teti. <br> | |

− | + | (ii) Compute the volumes of their queen's pyramids. <br> | |

− | + | (iii) Given their volume, how much bigger are the king's monuments? | |

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− | + | [[Category:Egyptian Mathematics Explorations]] | |

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## Latest revision as of 03:22, 10 February 2012

1. For the following pyramids compute the Seqed if possible.

Pyramid | Height | base | Seqed of the pyramid | Slope | Possible right triangle |
---|---|---|---|---|---|

Great Pyramid (Khufu) | 146.6 | 230.3 | 51.8 degrees | ||

Khafre | 143.5 | 215.25 | .75 | 53.1 degrees | 3-4-5 Triangle |

Menkaure | 66.45 | 103.4 | .79 | 51.3 degrees | Maybe 3-4-5 Triangle? |

Userkaf | 49 | 73.3 | 53 degrees | ||

Sahure | 48 | 78.5 | 50.5 degrees | ||

Queen Khentkawes | 72 | 25 | 52 degrees | ||

Djedkare | 52.5 | 78.75 | 52 degrees | ||

Djedkare's Queen | 21 | 41 | ca 45 degrees | ||

Teti | 52.5 | 78.5 | 53.1 degrees | ||

Teti's Queen (Iput) | 21 | 21 | 63 degrees |

3. Note the interesting difference between the pyramids of the Kings and those of the Queens. It is quite common for the Queens to have a much smaller pyramid.
The volume of a pyramid is given by <math>1/3 b^2 h</math>.

(i) Compute the volume the pyramids of Kings like Djedkare and Teti.

(ii) Compute the volumes of their queen's pyramids.

(iii) Given their volume, how much bigger are the king's monuments?