- Middle school๐Geometry๐บ
Volumes of cone, pyramid, and sphere: the 3 formulas
Cone/pyramid = (base ร height) / 3. Sphere = 4/3ยทฯยทrยณ. Three formulas for every middle-school solid.
- Middle school๐Geometry๐บ
A triangle's angles always sum to 180ยฐ
Why 180ยฐ? Cut the angles out with scissors โ they form a straight line. Proof in 3 animated steps.
- Middle school๐Geometry๐บ
Triangle area: half of the surrounding rectangle
Base ร height รท 2: the formula comes from a rectangle cut in half. The visual proof that makes the formula obvious.
- Middle school๐Geometry๐
Thales contrapositive: prove two lines are NOT parallel
If ratios aren't equal, lines aren't parallel. The contrapositive of the theorem.
- Middle school๐Geometry๐ญ
Thales' theorem: when triangles zoom
Two lines from the same point, cut by parallels. The lengths stay proportional. The key to measuring without measuring.
- Middle school๐Geometryโก๏ธ
Translation by a vector: the transformation that 'slides' everything
Every point moves by the same vector. No fixed point. Preserves everything (distances, angles, areas, orientation).
- Middle school๐คAlgebra๐งฉ
System of 2 equations, 2 unknowns: substitution that always works
Isolate, substitute, solve. The 3-step substitution method, with no sign-error risk.
- Middle school๐Trigonometry๐
SOH-CAH-TOA: the mnemonic that locks in sin, cos, tan in 30 seconds
Three letters, three rules, zero confusion. The middle-school method everyone remembers for right-triangle trig.
- Middle schoolโกMental math๐ฏ
Squaring a number ending in 5, without a calculator
Multiply the left part by itself + 1, stick 25 at the end. Done.
- Middle schoolโกMental mathยฑ
Signed numbers: the sign rule in 5 lines
Same sign = positive, different signs = negative. One rule for multiplication and division.
- Middle school๐ขArithmeticโ
Simplify a square root: hunting for perfect squares
โ72 = 6โ2 in 5 seconds. The method that pulls out perfect squares without breaking a sweat.
- Middle schoolโกMental mathโ
Simplify โa to bโc: pull out the largest perfect square
โ72 = โ(36 ร 2) = 6โ2. Find the largest perfect square dividing a and pull it out.