I wish I could give my two cents about that certain website, but if I did John Hammel would automatically give me the boot for using such foul and vulgar language

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If I had a million dollars, I'd bet that none of the "facts" presented on that site is true. The webmaster of that site likes to think that he has secrets, but come on now, Daughters of Zeus? Our sororities were founded on similar ideals of sisterhood, and the information you got from that site is pure rubbish. Comical and entertaining...but it's all manufactured!
We are not "daughters of" anyone nor do we have a patron goddess.
About Skiouros:
This comes directly from my new member manual. Skiouros comes from two Greek words meaning "shady" and "tail", and it was chosen by the Gamma chapter. This explanation of the squirrel's selection appeared in a 1915 publication:
"In the days when Gamma first made the triple colors of red, buff, and green her own, some of her energetic number sought a mascot to symbolize the characteristics of the colors and progress of Alpha Gamma Delta. In the autumn tints, so beautifully dear to us in our song of that name, they received the suggestion, and the little squirrel, typical frequenter of autumn haunts, was chosen as the mascot...Our little friend, we find, is also nimble and agile--he leaps from branch to branch and accomplishes much progress...to symbolize the spirit that never dies, the spirit of energetic alertness and progress."
...And that is why the squirrel is our mascot.