# 半立方抛物线

${\displaystyle x=t^{2}\,}$
${\displaystyle y=at^{3}.\,}$

${\displaystyle y^{2}-a^{2}x^{3}=0,}$

${\displaystyle y=\pm ax^{3 \over 2}.}$

${\displaystyle X=u^{2}}$
${\displaystyle Y=u^{3}.}$

## 性質

${\displaystyle x={3 \over 4}(2y)^{2 \over 3}+{1 \over 2}.}$

${\displaystyle x=3(t^{2}-3)=3t^{2}-9\,}$
${\displaystyle y=t(t^{2}-3)=t^{3}-3t.\,}$

## 參考資料

1. Pickover, Clifford A., The Length of Neile's Semicubical Parabola, The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Sterling Publishing Company, Inc.: 148, 2009, ISBN 9781402757969.
2. ^ Yoder, Joella G., Unrolling Time: Christiaan Huygens and the Mathematization of Nature, Cambridge University Press: 88, 2004 [2016-04-06], ISBN 9780521524810, （原始内容存档于2017-08-20）.
3. ^ Weisstein, Eric W. (编). Wolfram MathWorld (首頁). at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （英语）.
4. Carnahan, Walter H., Time Curves, School Science and Mathematics, 1947, 47 (6): 507–511, doi:10.1111/j.1949-8594.1947.tb06153.x.