A Natural Morphing Between Two Epicycloids
Year 2018,
, 68 - 77, 30.04.2018
Francisco Javier González Vieli
Abstract
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)
References
- [1] Bruce, J. W. and Giblin, P. J., Curves and singularities (2nd edition). Cambridge University Press, Cambridge, 1992.
- [2] Gomes Teixeira, F., Traité des courbes spéciales remarquables planes et gauches (reprint). Chelsea Publishing Company, New York, 1971.
- [3] Lockwood, E. H., A book of curves. Cambridge University Press, Cambridge, 1961.
- [4] Sewell, M., Parametric Envelopes. Math. Gazette 99 (2015), 226-229.
Year 2018,
, 68 - 77, 30.04.2018
Francisco Javier González Vieli
References
- [1] Bruce, J. W. and Giblin, P. J., Curves and singularities (2nd edition). Cambridge University Press, Cambridge, 1992.
- [2] Gomes Teixeira, F., Traité des courbes spéciales remarquables planes et gauches (reprint). Chelsea Publishing Company, New York, 1971.
- [3] Lockwood, E. H., A book of curves. Cambridge University Press, Cambridge, 1961.
- [4] Sewell, M., Parametric Envelopes. Math. Gazette 99 (2015), 226-229.
There are 4 citations in total.