Tosfos on 31b (continued from 31a) DH Amah writes that when the Gemara says a person is 3 Amos tall, it means that is his height up to his shoulders. However, when we include his head he is more than 3 Amos.
Tosfos garners support for this opinon from a Gemara in Eruvin 48a that say's a person's place is four Amos; his body is three Amos and another Amah is needed in order to take an object above his head. Tosfos contends that this means, a person's body is three full Amos, and another Amah is added to include his head, and his arms raised above his head.
How does Tosfos' find in this support for his opinion that the body is three full Amos without the head? In any normal person, when one sticks his hand all the way up, the elbow is at least as high as the head. Thus, he can reach a full Amah above his head! So according to Tosfos, we should add to the four Amos (three of his body, one of his arm) the amount that his head extends above his shoulders? If anything, it seems to that this Gemara supports the opinion that the body is three full Amos including the head!
Pesach Feldman, Yerushalayim
(a) First of all, I should point out that Tosfos is not providing support to his opinion from the Gemara in Eruvin. Rather, he is explaining that the Gemara in Eruvin does not contradict his opinion, and that it can be explained easily enough even according to his opinion.
This is clear from the words of Tosfos in Eruvin (48a DH Gufo). Tosfos starts by asking how the Gemara in Eruvin can contend that a person is 3 Amos tall whereas other Gemaras imply that a person is four Amos tall. After a number of other answers, he offers his novel explanation that the head is not included in the 3 Amos, and he contends that this can be the intention of the Gemara in Eruvin as well.
(b) As for why an outstretched arm does not add an Amah above one's head - Tosfos is being overly concise. A look into the Gemara in Eruvin eliminates your question.
Tosfos here is referring to two different opinions cited in Eruvin. One opinion maintains that a person's minimal "place" is 4 Amos in order to allow him to stretch his arms and legs. The second opinion maintains that his "place" is 4 Amos so that he can reach out and take an object from under his feet and place it under his head. The Gemara concludes that according to the first opinion, a person's "place" is actually longer than 4 Amos, and not exactly 4 Amos.
I think you will agree that your question is not applicable according to the second opinion in the Gemara in Eruvin, since that opinion does not mention stretching hands above the head. And according to the first opinion, the Gemara indeed says that we are referring to an area more than 4 Amos in length. (Note that the Gemara may not mean that the area is an entire head's-length longer than 4 Amos. The Gemara does not specify that a person must be given space to stretch his arms as far as he can ; just to stretch them above his head in a normal fashion.)
Best regards,
Mordecai Kornfeld
Kollel Iyun Hadaf