@mathchillguy: Engineers build entire bridges on the assumption that pi is basically 3, while mathematicians treat the rest of a Taylor expansion like a holy text that defines their entire personality. --------------------------------------- ➡️ The Taylor series struggle: ---------------- Taylor series approximations allow us to turn complex functions into simple polynomials. In the real world, f(x) = f(0) + f'(0)x is usually all you need to keep a bridge from falling down. Adding the f''(0)/2! * x^2 and higher terms is where the mathematical rigor kicks in, but let's be real: if you are calculating how much stress a beam can take, you stop caring about the third-order derivatives real quick. Mathematicians love the infinite sum because it is perfect; physicists just love it when the machine doesn't explode. Follow @mathchillguy for science breakdowns that never give you a tension headache. #mathchillguy #calculus #physicsmemes #engineering #stem

mathchillguy
mathchillguy
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Friday 11 September 2026 11:09:27 GMT
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claxmcb
ClaxMcb :
so um if u get into stochastic calculus, the second order piece becomes non-trivial and u need it for wiener processes to describe random stock price movements 🤓
2026-09-11 16:53:09
320
xknxwnnn
name man 🇵🇸🇪🇬 :
Who needs taylor series when you can use perturbation instead?
2026-09-11 15:18:44
89
me.probably.idk_2.0
me.probably.idk :
sin(x) = x confirmed
2026-09-11 21:11:17
147
zach.zeta.s
Zach.ζ(s) :
MacLaurin series ❌ Taylor series centered at zero ✅
2026-09-11 18:07:18
215
l_nba_script5
L_NBA_SCRIPT :
Physicists try not to be insufferable challenge: Level IMPOSSIBLE
2026-09-11 17:34:59
89
younm27
Yo :
That’s why so many engineering projects fail
2026-09-11 14:49:36
34
greg_from_accounting
⫍ ⃢👁ܫ👁⃢ ⫎ :
one might even say that "f(x)=y" is the superior form
2026-09-11 19:35:18
32
thecooperativeoperative
Co Op :
The real trick is understanding how accurate a given calculation needs to be. Engineering needs “good enough.” Real mathematical progress needs perfectly accurate.
2026-09-11 14:52:18
17
mrprettyflaco
mrprettyflaco :
“engineers… on the assumption that pi is basically 3” that’s very false and misleading
2026-09-11 23:49:52
1
homieswithsquidward
ToastIsFat :
I regret to inform you that if you get into numerical methods, simulation, or FEM that the 3rd and 4th terms become important again
2026-09-11 20:18:41
13
poopoo9999
𝙨𝙖𝙞𝙛𝙛𝙮𝙮𝙥𝙤𝙤𝙥𝙤𝙮 :
most phenomena really just need the first or second terms, rarely the third and beyond except for simulation/analytical results where error or precision is important
2026-09-11 17:51:15
7
user918876463
█████ :
Good one, good one
2026-09-14 01:18:02
0
dalfino_
andrew <3 :
sin(x) = x cos(x) = 1
2026-09-12 00:02:38
1
gasbug1
gasbug1 :
just use dual numbers f(x+ eps) = f(x) + eps*f'(x)
2026-09-11 22:08:00
2
crustaloid
Crustacean Advent Calendar :
Never understood Why transport/heat equations Are derived this way When using the Full Taylor expansion isn't that difficult
2026-09-11 17:12:07
0
wake.up8230
Wake up :
nah i agree with mathematicians
2026-09-14 10:57:04
1
el_alef_0
el alef cero :
in statistics also and you impress others saying "using first order of the Taylor" 😅
2026-09-11 16:29:38
2
papo_ishtar
papo_ishtar :
Solid state physicists definitely use the second and higher terms. The effective mass, used in characterization of the dynamics in semiconductors, is literally dependent on that second order term. Furthermore, any modeling as the extrema always loses its linear term (cuz it’s an extrema) so the second order is needed. Lastly, if you require parity conservation, you need more terms since you lose 1/2 of them.
2026-09-11 23:49:51
2
fupa81
fupa :
oh hun
2026-09-12 17:10:31
0
fishfunny123
fish :
we have computers that calculate this shit for us 😂
2026-09-12 02:48:52
0
xaltsc
alex :
it's just topology....
2026-09-14 18:17:59
0
world.wide.noon
v v v :
truly, we don't need this much precision
2026-09-14 07:20:59
1
jaxom_hartman
jaxom_hartman :
wait til you see the Taylor series expansion for spurious mixer products
2026-09-13 04:36:16
0
eigenvagrant
first order taylor approx. :
so true!!
2026-09-12 18:50:02
0
al465110
mokowmzs3pp :
Exponential map go brr
2026-09-11 14:54:10
0
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