Here are a few differences and similarities:
Difference: A pyramid is a tomb built to inter the body of a pharaoh. A gothic cathedral is a place of Christian worship built in honor of the Virgin Mary.
Similarity: A pyramid has wall paintings depicting the life of the pharaoh and images from the Book of the Dead. A gothic cathedral has stained-glass windows depicting stories from the Bible, with a large "rose" window.
Difference: Pyramids contained the material goods the pharaoh would need in the afterlife, including statuary, weapons, games, and the like. Gothic cathedrals contain relics of the saints and objects used in worship.
Similarity: All four sides of the Great Pyramid at Giza are aligned to the four cardinal compass points. Most gothic cathedrals are oriented to face the east, which is the direction from which Jesus said he will rise again.
Similarity: The pyramids were built in the shape of a sacred object--the benben stone, which is where Egyptians believed the sun first shone and the world was created. Gothic cathedrals were built in the shape a sacred object--the cross on which Jesus was crucified.
Difference: Pyramids were sealed for eternity (that is, until tomb robbers and archaeologists broke in). Cathedrals are open to the public for worship and other activities.
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Certain ingredients of English Gothic architecture not only added aesthetically to the cathedrals, but were structural innovations as well. "The first was the pointed arch. This was the point at which the top of the columns meet. Having them meet at an angle added strength. The second was the vaults. These were the internal supports of the cathedral ceiling. Rib vaults replaced single pointed vaults, increasing both the strength and beauty of the cathedral. Last the flying buttress. "Flying buttress assisted in carrying the thrust of the vaults. "This external feature is an example of a functional addition to cathedral design that was also ornate and beautiful." A pyramid is a "massive stone or brick structure with a square base and four sloping triangular sides that meet in a point at the top. For over one thousand years Egyptian kings built tombs for themselves and their queens in the form of pyramids. There are over ninety 'royal' pyramids in Egypt. The first true pyramid was constructed for King Snefru at Medium. The burial chamber was only accessible by a small tunnel in the north face with a 28 degree slope. The famous bent pyramid at Dahshur has sides that originally sloped at 54 degrees. Midway through the project, cracks began to appear due to the steep slope. From this point on, architects changed the slope to a gentler 43 degrees, which became the standard for all pyramids.