Commit 84e682ec authored by bBoesl's avatar bBoesl

pyramid

parent 251b2a8a
......@@ -19,7 +19,7 @@ theory Vector : http://mathhub.info/MitM/Foundation?Math =
// include ☞algebra:?RealVectorspace ❙
vector: type ❘ # V ❙
// vector: type ❘ = realVec3.universe❘ # V ❙ // works but is slow as sloth ❙
// vector: type ❘ = realVec3.universe❘ # V ❙ // works but is slow as sloth ❙
vectorOf: ℝ ⟶ ℝ ⟶ ℝ ⟶ V ❘ # Vof 1 2 3 ❙
OV : V ❙
v_1: V ⟶ ℝ ❘ # _x 1 prec 50 ❙
......
namespace http://BenniDoes.Stuff/ ❚
import mitm http://mathhub.info/MitM/Foundation ❚
import arith http://mathhub.info/MitM/smglom/arithmetics ❚
theory Pyramid : http://mathhub.info/MitM/Foundation?Math =
include ☞http://BenniDoes.Stuff/?Vector ❙
include ☞http://BenniDoes.Stuff/?Triangle ❙
Pyramid : type ❘ # Pyr ❙
pyramidOf : V ⟶ V ⟶ V ⟶ V ⟶ Pyr ❘ # Pyrof 1 2 3 4 ❙
P_A : Pyr ⟶ V ❘ # P_A 1❙
P_A_axiom : {a :V, b :V, c :V, dd :V } ⊦ ( P_A ( Pyrof a b c dd) ) ≐ a ❙
P_B : Pyr ⟶ V ❘ # P_B 1❙
P_B_axiom : {a :V, b :V, c :V, dd :V } ⊦ ( P_B ( Pyrof a b c dd) ) ≐ b ❙
P_C : Pyr ⟶ V ❘ # P_C 1❙
P_C_axiom : {a :V, b :V, c :V, dd :V } ⊦ ( P_C ( Pyrof a b c dd) ) ≐ c ❙
P_D : Pyr ⟶ V ❘ # P_D 1❙
P_D_axiom : {a :V, b :V, c :V, dd :V } ⊦ ( P_D ( Pyrof a b c dd) ) ≐ dd ❙
Volume_Pyramid: Pyr ⟶ ℝ ❘ = [p ] ( 1 / 6) ⋅ ( < ( ( ( P_B p ) ⁻ ( P_A p ) ) Vcross ( ( P_C p ) ⁻ ( P_A p ) ) ), (( P_D p ) ⁻ ( P_A p ) ) > ) ❘# VolofP 1 ❙
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......@@ -15,6 +15,6 @@ theory Sphere : http://mathhub.info/MitM/Foundation?Math =
collidesSphereLine: S ⟶ L ⟶ bool ❘ = [s,l] ∃ [v] ( v VonL l ) ∨ (v VinS s ) ❘ # 1 ScolL 2 ❙
circumfenceSphere: S ⟶ ℝ ❘ = [s] ( Sr s ) ⋅ 2 ⋅ π ❘ # CS 1 ❙
areaSphere : S ⟶ ℝ ❘ = [s] ( Sr s ) ⋅ ( Sr s ) ⋅ π ❘ # AS 1 ❙
circumfenceSphere: S ⟶ ℝ ❘ = [s] ( Sr s ) ⋅ ( Sr s) ⋅ 4 ⋅ π ❘ # CS 1 ❙
areaSphere : S ⟶ ℝ ❘ = [s] ( Sr s ) ⋅ ( Sr s ) ⋅ (Sr s) ⋅ ( 4 / 3 ) ⋅ π ❘ # AS 1 ❙
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