3. Lemma: introduction to inverse Pythagorean Theorem
Assume △ ABC is a right triangle with ∠ c=90 ゜ and h is the height from C to AB.
The inverse Pythagorean Theorem states that,
1 ℎ 2
= 1
+ 1
2
2
Proof: a × b=c × h=2s
2 2 ∗ 2
= 1 ℎ
= 1
→
ℎ 2
2 = 2 + 2
2 + 2 2 ∗ 2
= 1
ℎ 2
1 2
+ 1
= 1
2
ℎ 2
4. Inverse-square Law
The inverse-square Law, in physics, is any physical law starting that a specified physical quantity or
intensity is inversely proportional to the square of the distance from the source of that physical quantity.
Mathematically notated
1 2
Intensity ∝
【 2 】
According to the inverse Pythagorean Theorem, if we place three same bulbs (assume all of their brightness
are unit 1) at A, B and H.
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