Исследование свойств прямоугольного тетраэдра

Доклад - Математика и статистика

1 (r; r; r) :

___ __

= |1|cos? , ? 1 .

___ __ _ __ _

|OO1|cos? = (OO1do) = rcos? + rcos? + rcos? , (1d) .

= h,

h = OK + KH, ..

h = |OO1|cos? + r, .. = r

( 1 ).

h = r cos? + r cos? + r cos? + r

r = h / (1 + cos? + cos? + cos?)

4- 5- :

____________

(abc)/vab+bc+acabc

r = ____________ = ____________ ,

1 + (bc + ac + ab) / vab+bc+ac vab+bc+ac + ab + bc + ac

= = =

___

v1/3

_________ __

= v +OC = v2

_________ __

= v +OB = v2

_________ __

= v + = v2

.. , .

. . ,

_ _ _ ___

= (v3/2) = (v3/2)v2 = v3/2

, . :

= /v2

: __

os _ = / = 1/v3 , .

: 8 .