Find the shape inside the data.

For the entered points one comma one, two comma one and three comma one, the mean is two comma one. Centering gives x offsets minus one, zero and one, and all y offsets zero. The source sums squared x offsets to two, squared y offsets to zero and cross products to zero. Its half arctangent formula gives zero degrees and the largest eigenvalue share is one hundred percent. The geometry uses one hundred pixels per coordinate unit. The actual page draws the input cloud and principal direction line, but does not display the projected one dimensional scores. Now enter one comma one, two comma two and three comma three. The centered offsets are minus one minus one, zero zero and one one. The source squared sums are two and two and the cross sum is two. Half arctangent of four and zero gives forty five degrees. The largest eigenvalue is four out of total four, so the source share is one hundred percent. Points use the same one hundred pixels per coordinate unit in both axes; screen y is inverted. This illustrates this local formula, not a fitted external dataset or an independent statistical study. For those diagonal points, the source computes distances from point one as zero, square root two and two times square root two. Bars use one hundred pixels per distance unit, so lengths are zero, about one hundred forty one point four and two hundred eighty two point eight pixels. This animation shows that computed array. The actual MDS canvas instead redraws the original input points and does not use the distance array for a new embedding. It is not a full multidimensional scaling algorithm or an all-pairs distance layout. The fixed downloaded study note gives point count, direction and share, and its broad MDS wording does not change this implementation limit.