Update README.md

README.md

@@ -145,7 +145,7 @@ Evaluation performed using **Adaption Labs AutoScientist**
 
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-# 🧠 Mathematical Knowledge
+# Mathematical Knowledge
 
 This model is optimized to solve a broad range of mathematical problems through logical reasoning instead of memorization.
 
@@ -171,4 +171,33 @@ It performs best when explaining every intermediate step before arriving at the
 | Numerical Analysis | Approximation Methods |
 | Differential Equations | Ordinary and Partial Differential Equations |
 
-
+##  Fundamental Mathematical Formulae
+
+| Formula | Equation |
+|---------|----------|
+| Quadratic Formula | $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ |
+| Pythagorean Theorem | $a^2+b^2=c^2$ |
+| Distance Formula | $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ |
+| Midpoint Formula | $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$ |
+| Slope Formula | $m=\frac{y_2-y_1}{x_2-x_1}$ |
+| Point-Slope Form | $y-y_1=m(x-x_1)$ |
+| Equation of a Line | $y=mx+b$ |
+| Area of Circle | $A=\pi r^2$ |
+| Circumference | $C=2\pi r$ |
+| Volume of Sphere | $V=\frac43\pi r^3$ |
+| Surface Area of Sphere | $A=4\pi r^2$ |
+| Volume of Cylinder | $V=\pi r^2h$ |
+| Volume of Cone | $V=\frac13\pi r^2h$ |
+| Euler's Formula | $e^{ix}=\cos x+i\sin x$ |
+| Euler's Identity | $e^{i\pi}+1=0$ |
+| Bayes' Theorem | $P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$ |
+| Arithmetic Mean | $\bar{x}=\frac{x_1+\cdots+x_n}{n}$ |
+| Geometric Mean | $GM=\sqrt[n]{x_1x_2\cdots x_n}$ |
+| Harmonic Mean | $HM=\frac{n}{\sum\frac1{x_i}}$ |
+| Standard Deviation | $\sigma=\sqrt{\frac{\sum(x-\mu)^2}{N}}$ |
+| Variance | $\sigma^2=\frac{\sum(x-\mu)^2}{N}$ |
+| Derivative | $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$ |
+| Integration by Parts | $\int u\,dv=uv-\int v\,du$ |
+| Chain Rule | $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$ |
+| Product Rule | $(uv)'=u'v+uv'$ |
+| Quotient Rule | $\left(\frac uv\right)'=\frac{u'v-uv'}{v^2}$ |