PIRAMIDA SA VIDIKOVCEM
Piramida je poliedar omeđen osnovom i stranicama koje se spajaju u jednoj tački – temenu, koje se nalazi na suprotnoj strani od osnove. Piramida može biti pravilna ili nepravilna. Pravilna piramida je ona kod koje osnovu čini pravilan mnogougao. Piramida, takođe, može biti prava ili kosa. Prava piramida je ona kod koje se projekcija temena na osnovu poklapa sa težištem osnove. Površina piramide jednaka je zbiru površina osnove i stranica. Osnova može biti bilo koji mnogougao, dok su stranice zapravo trouglovi.
Apotema (engl. Apothem) je prostor u geometrijskim figurama, najčešće piramidi ili prizmi, koji označava visinu stranice njihovog omotača (M). Broj apoteme može biti od velikog značaja za određivanje površine ili zapremine piramide ili nekog drugog geometrijskog tela. Redovni poligoni su jedini poligoni koji imaju apotheme. Zbog toga, sve apoteme poligona će biti podudarne. Za redovne piramide, što je piramida čija osnova je redovan poligon, apotema je visina nagiba bočnih strana, to jest, najkraće rastojanje od temena do ivice poligona. Za jednakostranični trougao, apotema ekvivalentna je duži od sredine jedne strane za svaki od centara trougla, pošto se centri jednakostraničnog trougla poklapaju kao posledica definicije. Pravilna četvorostrana piramida u osnovi ima kvadrat stranice a. Omotač te piramide sačinjavaju četiri jednakokraka trougla osnovice a, krak s i visina H.
Zanimljivosti
1. Piramide su tako pozicionirane da nijedna ne stvara senku drugoj. Za izgradnju ovih piramida bili su potrebni brojni matematički proračuni, kao i pomno astronomsko posmatranje, jer je svaka njihova stranica okrenuta određenoj strani sveta.
2. Ukoliko kvadriramo visinu piramide, dobićemo vrednost površine njenih stranica.
3. Piramida je džinovski peščani sat. Senke koje ona stvara od sredine oktobra do početka marta prikazuju godišnja doba i dužinu jedne godine. Dužina kamenih ploča koje se nalaze oko piramide, odgovara dužini senke u jednom danu
.4. Dosetljivi Tales. Postoji nekoliko zapisa o tome kako je Tales izračunao visinu piramida. Preko dana čekao je trenutak kada će senka svih predmeta (npr. štapa koji je zabio u pesak pokraj piramide) biti jednaka njihovoj visini. To je onda primenio i na piramidu i preko senke izračunao njenu visinu.



A PYRAMID WITH A VIEW

 

A pyramid is a polyhedron formed by connecting a polygonal base and a point – the apex, which is on the opposite side of the base. A pyramid can be right or non-right. A right pyramid is the one with a regular polygon base. A pyramid can also be right or oblique. A right pyramid has its apex directly above the centroid of its base. The surface area of a pyramid equals the sum of the surface area of the base and faces. The base can be any polygon, while faces are actually triangles.

An apothem is the space in geometric figures, most often in a pyramid or a prism, which denotes the perpendicular line or distance from the centre of a regular polygon to any of its sides (M). The value of the apothem can be of great importance for determination of the surface area or the volume of the pyramid or any other geometric shape. Regular polygons are the only polygons with an apothem. Therefore all apothems of a polygon are identical. For the right pyramid, the base of which is a regular polygon, the apothem is the height of the inclination of faces, that is, the shortest distance from the apex to the edge of the polygon. For the equilateral triangle, the apothem is equivalent to the line segment from the middle of one face for each of the centres of the equilateral triangle because the centres of the equilateral triangle are identical according to the definition. A regular square pyramid has a square with the side a as its base. The net of the pyramid is comprised of four equilateral triangles of the perimeter a, a leg s and the height H.

Interesting facts

  1. The pyramids are arranged in such a way that none of them casts a shadow on another. Numerous mathematical calculations were needed for building these pyramids, as well as astronomical observation, because each of their sides is turned to another side of the world.
  2. If we square the height of a pyramid, we will get the sum of the surface area of its faces.
  3. A pyramid is a giant sundial. A pyramid creates shadows from the middle of October to the beginning of March which display seasons and the length of a year. The length of stone slabs that surround the pyramid corresponds to the length of a shadow in one day.
  4. Witty Thales. There are several records on how Thales had calculated the height of a pyramid. He was waiting for the moment when the shadow of an object (for example, of a stick spiked in the sand by the pyramid) was equal to its height. It applied the same principle to the pyramid and calculated its height using the length of its shadow.