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♥️ I LOVE ALLAH♥️
#خاتم_النبیین_محمدﷺ#درود_وقرآن
MIT filmed a multivariable calculus lecture in 2007 that answers a question almost nobody asks: what path does the valve cap on a bike wheel actually trace. 330 thousand views in 17 years.
it is free on YouTube. lecture 5 of 18.02, parametric equations for lines and curves, taught by Denis Auroux.
his point: a curve is not a graph. it is a moving point. write position as a function of time and geometry turns into kinematics. y = f(x) cannot describe a loop. r(t) can.
at the board it's simple. a line through Q and R is r(t) = Q + t(R − Q). substitute that into the equation of a plane and the intersection becomes one equation in one unknown, t. that is the whole of ray-plane intersection.
then the wheel. roll a circle of radius a along the ground and track one point on the rim. x = a(θ − sin θ), y = a(1 − cos θ). two lines. no picture required.
the good part is at the bottom. the slope is dy/dx = sin θ / (1 − cos θ). take two Taylor terms: sin θ ≈ θ and 1 − cos θ ≈ θ²/2. so dy/dx ≈ 2/θ, and it blows up. the curve is vertical at the cusp, not smooth, and near it y grows like x^(2/3), not like x².
that cusp is a physical statement. the contact point of a rolling wheel is momentarily at rest. same curve is the brachistochrone, the shape Huygens hung his pendulum on, the profile old gear teeth were cut to.
the math is free and public. so is the lecture. what nobody can sell you is the habit of testing a curve with two terms of a series instead of trusting the drawing. that habit is built over a semester, not one video.
Divino Niño Jesús, dueño de mi corazón, te entrego mi día, mis preocupaciones y mis alegrías.
En tu infinita ternura confío. Bendice mi hogar y haz que mi corazón sea tan puro y humilde como el tuyo.
Amén."
#oracionaldivinoniñojesus
$NEAR has spent multiple years building a massive base after completing a full Elliott Wave correction.
The chart suggests that Waves (1) through (4) are already complete, with price repeatedly defending the same long-term liquidity pool.
That support zone has held through multiple market cycles, making it one of the strongest technical areas on the entire chart.
Historically, major impulsive moves often begin after this type of prolonged accumulation.
If Wave (5) starts to develop as expected, $NEAR could enter its strongest expansion phase since launch.
The current structure remains constructive as long as price continues to hold above the long-term support.
The projected fifth wave points toward the $24+ region, which aligns with the previous cycle’s major resistance.
That would represent a move of roughly +3,240% from the current price.
The path higher is unlikely to be linear.
Pullbacks, consolidations, and periods of volatility should be expected throughout the move, but they would be normal within a larger impulsive trend.
A confirmed increase in volume together with higher highs and higher lows would add further confidence that Wave (5) is officially underway.
If that scenario plays out, $NEAR could become one of the strongest-performing large-cap altcoins of the next market cycle.