why calculus is necessary in architecture....

Background info:-
Historically, architecture has been a part of mathematics , so much so the two disciplines were distinguishable. Ancient architects were mathematicians as well. Throughout time , architects have created mathematically amazing structures such as;
temples, pyramids, ziggurats , and integration projects. Architects could use simple geometry
if buildings were simple squares and triangles, but a vast majority of buildings involve curves
and strange angles-this is where calculus comes into play.

Applications of Calculus:-

Calculus can be utilized by architects to express design plans through graphs or drawings . They can
mathematically describe surfaces for the adaptation of drawings to computer software. This can be
done through various integral equations. Calculus was used in the designing and construction of the
mathematically sound Eiffel Tower. In addition to accurately depicting the layout of the building,
calculus also is used to find the volume and surface area of buildings for their building requisites, as
well as to find the specifications for acoustics within a buildings.

Derivatives in use:

Although the tower looks complex ,surprisingly, it can be graphed with two simple equations;
𝑦=𝑒^𝑥
𝑦=−𝑒^(−𝑥)
As the tower was being built, wind became a major concern for the architects . But by utilizing
calculus they found the tangent lines of the towers main curves (their derivatives).The tangent lines
were used to locate the center of the tower or where its mass is focused. By knowing this center
the architects balanced the tall structure by using wind as an ally instead of an obstacle. Thus, the
tower was molded by wind.

Integral Calculus in use:-

Many factors come into play when an architect designs a building. Ascetics, lighting, size, and even heating are taken into consideration .If an architect is
focusing on the heating of his/her structure and wants to figure out how much heat is being
lost based on temperature variations throughout the day ,they can utilize calculus. They can
graph heat loss vs time and find the area under the curve . This area can be found by evaluating
a definite integral and finding the area between the curve and the x-axis.

Surface area/Volume:-
Calculus is used to find the area under a curve, or the area of two intersecting curves, as seen
In the Athenaeum . This is important because with the area and surface volume architects will
Then calculate the amount of materials needed, as well as the cost of the project. Using integral
Calculus to calculate area and volume.
area, A=∫𝑎^𝑏▒〖𝑦𝑑𝑥=∫𝑎^𝑏▒∫1▒〖(𝑥)〗 𝑑𝑥,〗

When Calculus is neglected:-

A well-known example of design plan gone wrong is the Leaning Tower of Pisa .The building
Was originally intended to stand upright , but the weight was not accounted for and early on
in its construction began leaning over. Wet soil and decay have caused the structure to
Sink downward and tilt. The tower is just one example of a neglecting the math and integral
Calculus that goes along with the architecture process.