The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
This is known as the proportional segments theorem, or the fundamental theorem of similarity, and for triangle ABC, with line segment DE parallel to side AB, the theorem corresponds to the mathematical expression CD/DA = CE/EB.
With the introduction of Ω, the projected figure corresponds to a theorem discovered by Menelaus of Alexandria in the 1st century ad C′D′/D′A′ = C′E′/E′B′ ∙ ΩB′/ΩA′.Since the factor ΩB′/ΩA′ corrects for the projective distortion in lengths, Menelaus's theorem can be seen as a projective variant of the proportional segments theorem.
A differentially coloured horizontal bar is displayed for each chromosomal segment, with a length proportional to the expression value assigned to the relative segment.
We therefore examined associations of maternal and paternal anthropometry [height and body mass index (BMI)] with offspring characteristics including birthweight, head circumference, absolute and proportional limb segment and trunk lengths, and skinfolds.
We tested whether parents' prepregnancy height and body mass index (BMI) were related to neonatal anthropometry (birthweight, head circumference, absolute and proportional limb segment and trunk lengths, subcutaneous fat) among 1,041 Australian neonates using stepwise linear regression.
We propose that the value of Tcnt is inversely proportional to the segment separation between the sender of the warning message and the segment leader (i.e., the receiver): T cnt = ( M max − M s, r ) T slot, (3).
The polyalanine expansion in the N-terminal peptide of PABPN1 induces the formation of an alpha-helical segment proportional in size to the number of alanines in expansion.
The magnitude of HPV in vivo is inversely proportional to lung segment size.
