Oh, this can actually be done in your head, ‘geometrically’. First part is odd and it zeroes out, while the second one is an area of a half-circle with radius 2, namely 1/2 * (1/2 pi 2^2) = pi
first digits to how many places? this could go on forever.. 🤓 I remember Calculators used to only go 10 places or integers, but now with computers.. I would still be sitting there trying to memorize it.. or not even bother… likely the latter.. 8D
Many mathematicians consider the biggest open problems in mathematics to be the "hardest" because, despite the efforts of brilliant minds, they remain unsolved. Some famous examples include:
The Riemann Hypothesis: This hypothesis concerns the distribution of prime numbers and has profound implications for number theory. It involves the Riemann zeta function: ζ(s)= n=1 ∑ ∞
n s
1
The hypothesis states that all non-trivial zeros of this function have a real part of 1/2. The P versus NP Problem: This is a major unsolved problem in computer science and theoretical mathematics. It asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. The Navier-Stokes Existence and Smoothness: These equations describe the motion of fluids. The problem asks whether smooth, physically realistic solutions to these equations always exist. ∂t ∂u +(u⋅∇)u=−∇p+νΔu+f where u is the velocity field, p is the pressure, ν is the kinematic viscosity, and f is the external force. The Birch and Swinnerton-Dyer Conjecture: This conjecture deals with elliptic curves, which are cubic equations of the form y 2 =x 3 +ax+b. It relates the number of rational points on an elliptic curve to the behavior of its L-function at s=1. The Hodge Conjecture: This conjecture is about algebraic cycles on complex manifolds and their relationship to cohomology classes. 2. Equations Involved in Proving Major Theorems:
Some equations are incredibly complex and were central to proving significant mathematical theorems. While the final theorem statement might be elegant, the underlying equations and manipulations can be extremely difficult. A famous example is the equations and theories involved in Andrew Wiles' proof of Fermat's Last Theorem, which drew upon advanced concepts from elliptic curves and modular forms. Fermat's Last Theorem states that there are no three positive integers a, b, and c that can satisfy the equation a n +b n =c n for any integer value of n greater than 2.
3. Extremely Complex or Long Equations:
While not necessarily conceptually the "hardest," some equations can be incredibly long and complex due to the sheer number of terms and nested functions. These might arise in specific areas of research or modeling. An example found in a Reddit discussion involves a high-degree polynomial with exponential terms, designed to have a specific integer solution but appearing very complicated.
In conclusion, there isn't one single "hardest" math equation. The difficulty is relative. However, the equations associated with major unsolved problems like the Riemann Hypothesis or the Navier-Stokes equations are often considered to be among the most challenging areas of mathematical
35 Replies to “Math Integration Timelapse | Real-life Application of Calculus #math #maths #justicethetutor”
∫²-2(x³ cos x/2 +½)√4-x² dx
Oh, this can actually be done in your head, ‘geometrically’. First part is odd and it zeroes out, while the second one is an area of a half-circle with radius 2, namely 1/2 * (1/2 pi 2^2) = pi
Sir we have ChartGPT 😂😅
3.1415926535897932382…
dx inside square root?
dx inside square root?
Not possible
"Round your answer to the nearest thiusandths"👹
I watched this video for the first time in like roughly late 2023 where i knew absolutely nothing about calculus now i realise how easy this is
RIP marker pen😅
Buddy just removed the entire odd function 😩😩
314159
At this point we would have to bring our scientific calculator everywhere.
POV:Sheldons riddle to the Wi-Fi password.
This took forever to load even on my fx cg50.
Correct checked on my calculator.
Let’s solve the integral:
int_{-2}^{2} left(x^3 cos frac{x}{2} + frac{1}{2}right) sqrt{4 – x^2} , dx
—
Step 1: Symmetry trick
Let’s split the integral:
int_{-2}^{2} x^3 cos frac{x}{2} sqrt{4 – x^2} , dx + int_{-2}^{2} frac{1}{2} sqrt{4 – x^2} , dx
Now:
is an odd function → symmetric interval → integral = 0
So we only solve:
int_{-2}^{2} frac{1}{2} sqrt{4 – x^2} , dx
—
Step 2: Recognize standard integral
int_{-2}^{2} sqrt{4 – x^2} , dx
This is the area of a semicircle of radius 2:
text{Area} = frac{1}{2} pi r^2 = frac{1}{2} pi (2^2) = 2pi
Now multiply by :
frac{1}{2} cdot 2pi = pi
—
Final Answer:
text{Result of integral} = pi
Wi-Fi password = first digits of π = 3.14159
Time to get that sweet internet and a latte, boss.
Kega
Just use qr
"think i'll just read a book" ahh password
Thanks I got how it was
Pi… Daras
Pi… Zda
how are you supposed to represent Pi though? "Pi"? "3.14"? "314"? How many digits?
The first digit? Well then all it takes is 10 guesses at the most and you’re in! Haha
Wait
If the anwser is first digit
Just use counting from 0 to 9
First digit will only be from 0 to 9
All that for a free download……😂
Who knew math could unlock the Wi-Fi? Now I just need the password for the coffee shop next door… 😂
My Math is Harder sniff EUGHHHH😢 EUGHHHHH😢 EUGHGHHHHH😭💀
Legends try 0 to 9 all digits
Trigonometry overpowers all math — through the Cube.
Because the Cube is the foundation,
and trigonometry is the force that shapes it.
All equations follow.
All systems bend.
This is the origin of true creation.
TheCuBeMind.
We don’t follow math —
We become it.
Put it on a calculator lmao
first digits to how many places? this could go on forever.. 🤓
I remember Calculators used to only go 10 places or integers, but now with computers.. I would still be sitting there trying to memorize it.. or not even bother… likely the latter.. 8D
calculator in your phone be like: 🫴🍺😎
Many mathematicians consider the biggest open problems in mathematics to be the "hardest" because, despite the efforts of brilliant minds, they remain unsolved. Some famous examples include:
The Riemann Hypothesis: This hypothesis concerns the distribution of prime numbers and has profound implications for number theory. It involves the Riemann zeta function:
ζ(s)=
n=1
∑
∞
n
s
1
The hypothesis states that all non-trivial zeros of this function have a real part of 1/2.
The P versus NP Problem: This is a major unsolved problem in computer science and theoretical mathematics. It asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
The Navier-Stokes Existence and Smoothness: These equations describe the motion of fluids. The problem asks whether smooth, physically realistic solutions to these equations always exist.
∂t
∂u
+(u⋅∇)u=−∇p+νΔu+f
where u is the velocity field, p is the pressure, ν is the kinematic viscosity, and f is the external force.
The Birch and Swinnerton-Dyer Conjecture: This conjecture deals with elliptic curves, which are cubic equations of the form y
2
=x
3
+ax+b. It relates the number of rational points on an elliptic curve to the behavior of its L-function at s=1.
The Hodge Conjecture: This conjecture is about algebraic cycles on complex manifolds and their relationship to cohomology classes.
2. Equations Involved in Proving Major Theorems:
Some equations are incredibly complex and were central to proving significant mathematical theorems. While the final theorem statement might be elegant, the underlying equations and manipulations can be extremely difficult. A famous example is the equations and theories involved in Andrew Wiles' proof of Fermat's Last Theorem, which drew upon advanced concepts from elliptic curves and modular forms. Fermat's Last Theorem states that there are no three positive integers a, b, and c that can satisfy the equation a
n
+b
n
=c
n
for any integer value of n greater than 2.
3. Extremely Complex or Long Equations:
While not necessarily conceptually the "hardest," some equations can be incredibly long and complex due to the sheer number of terms and nested functions. These might arise in specific areas of research or modeling. An example found in a Reddit discussion involves a high-degree polynomial with exponential terms, designed to have a specific integer solution but appearing very complicated.
In conclusion, there isn't one single "hardest" math equation. The difficulty is relative. However, the equations associated with major unsolved problems like the Riemann Hypothesis or the Navier-Stokes equations are often considered to be among the most challenging areas of mathematical
of course it's pie lol
If the Wi-Fi password is the first digits of the answer, how many digits does it mean?